It is our aim to prove strong convergence of a new iterative sequence to a common element of the solution set of a generalized mixed equilibrium problem; the null space of an inverse strongly monotone operator; the set of common fixed points of a countable infinite family of nonexpansive mappings; and the set of fixed points of a continuous pseudocontractive mapping. Moreover, the common element is also a unique solution of a variational inequality problem and optimality condition for a certain minimization problem. Our theorems generalize, improve, and unify several recently announced results.

Eric U. Ofoedu

A General Approximation Scheme for Solutions of Various Problems in Fixed Point Theory

We introduce the concepts of generalized relaxed monotonicity and generalized relaxed semimonotonicity. We consider a class of generalized vector variationa-llike inequality problem involving generalized relaxed semimonotone mapping. By using Kakutani-Fan-Glicksberg&#x2019;s fixed-point theorem, we prove the solvability for this class of vector variational-like inequality with relaxed monotonicity assumptions. The results presented in this paper generalize some known results for vector variational inequality in recent years.

Suhel Ahmad Khan

Vector Variational-Like Inequalities with Generalized Semimonotone Mappings

A new identity for resolvents of operators is suggested. We show that in appropriate
situations it is more convenient than the Hilbert identity. In particular, we establish a new
invertibility condition for perturbed operators as well as new bounds for the spectrum of
perturbed operators. As a particular case we consider perturbations of Hilbert-Schmidt
operators.

Michael Gil'

A New Identity for Resolvents of Operators

We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.

H. Mazaheri

S. A. M. Mohsenalhosseini

Approximate Equilibrium Problems and Fixed Points

In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.

Daniela Paesano

Pasquale Vetro

Common Fixed Points in a Partially Ordered Partial Metric Space

This paper studies the instability of the zero solution for a certain nonlinear functional vector differential equation of the seventh order with multiple deviating arguments. Under sufficient conditions, we prove a result on the instability of the zero solution. This work contributes and complements to previously known results in the literature.

Cemil Tun&#xe7;

On the Unstable Solutions to Functional Vector Differential Equations of the Seventh Order

Some existence and convergence theorems for a class of nonexpansive type mappings are obtained in a normed space. The results obtained herein generalize certain known results.

S. N. Mishra

Rajendra Pant

R. Panicker

Some Existence and Convergence Theorems for Nonexpansive Type Mappings

In 2012, the notion of <svg     style="vertical-align:-0.1638pt;width:9.7749996px;" id="M3" height="7.9499998" version="1.1" viewBox="0 0 9.7749996 7.9499998" width="9.7749996"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D6FC"/></g>

		
	
</svg>-<svg     style="vertical-align:-3.56265pt;width:11.2375px;" id="M4" height="13.225" version="1.1" viewBox="0 0 11.2375 13.225" width="11.2375"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,8.737)"><use xlink:href="#x1D713"/></g>

		
	
</svg>-contractive type mappings was introduced by Samet, C. Vetro, and P. Vetro. By using a simple method, we give some coupled fixed point results for <svg     style="vertical-align:-0.1638pt;width:9.7749996px;" id="M5" height="7.9499998" version="1.1" viewBox="0 0 9.7749996 7.9499998" width="9.7749996"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D6FC"/></g>

		
	
</svg>-<svg     style="vertical-align:-3.56265pt;width:11.2375px;" id="M6" height="13.225" version="1.1" viewBox="0 0 11.2375 13.225" width="11.2375"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,8.737)"><use xlink:href="#x1D713"/></g>

		
	
</svg>-contractive type mappings.

Sh. Rezapour

J. Hasanzade Asl

A Simple Method for Obtaining Coupled Fixed Points of <svg style="vertical-align:-0.1638pt" height="7.9499998" version="1.1" viewBox="0 0 9.7749996 7.9499998" width="9.7749996" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D6FC" d="M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204&#xA;q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z" /></g></svg>-<svg style="vertical-align:-3.56265pt" height="13.225" version="1.1" viewBox="0 0 11.2375 13.225" width="11.2375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,8.737)"><path id="x1D713" d="M642 419q-50 -36 -71 -94q-28 -78 -68 -170q-39 -89 -114 -135q-34 -21 -83 -31l-45 -219l-31 -31q-8 7 -15 29.5t-2 45.5l35 172q-153 10 -153 169q0 28 6 84q7 68 7 88q0 48 -27 48q-18 0 -51 -28l-7 26q62 75 118 75q49 0 49 -90q0 -47 -5 -81q-10 -72 -10 -108&#xA;q0 -117 82 -133l87 455l62 19l7 -2l-99 -478q91 12 131 120q34 93 51 154q20 73 36 88q42 40 103 56z" /></g></svg>-Contractive Type Mappings

We are concerned with finding a class of weight functions <svg style="vertical-align:-3.56265pt;width:9.8000002px;" id="M1" height="12.175" version="1.1" viewBox="0 0 9.8000002 12.175" width="9.8000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D454" d="M546 430q-14 -33 -37.5 -140t-38.5 -209q-29 -195 -156 -289q-29 -21 -70 -37t-78 -16q-62 0 -102.5 37t-40.5 69q0 27 26 48q19 15 25 -3q13 -43 46.5 -69t87.5 -26q55 0 83 21q29 22 50 65t43 140q14 64 29 163h-2q-55 -81 -149 -152q-59 -44 -102 -44q-23 0 -43.5 30&#xA;t-20.5 85q0 74 32.5 145.5t84.5 117.5q40 35 100 58.5t117 23.5q21 0 65 -8q30 -6 44 -6zM456 386q-40 16 -81 16q-29 0 -64 -13q-42 -17 -85 -97q-19 -36 -31.5 -86t-12.5 -86q0 -64 30 -64q20 0 52.5 21t60.5 52q74 81 95 123q26 62 36 134z" /></g></svg> so that the following generalized Hardy-Sobolev inequality holds: <svg style="vertical-align:-5.79437pt;width:218.83749px;" id="M2" height="23.049999" version="1.1" viewBox="0 0 218.83749 23.049999" width="218.83749" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.788)"><path id="x222B" d="M480 853q0 -20 -13.5 -32.5t-34.5 -12.5q-19 0 -34.5 18t-27.5 18q-13 0 -21 -11.5t-13 -50.5t-4 -109l6 -574q6 -488 -183 -488q-28 0 -46.5 16t-18.5 38q0 19 14 32.5t33 13.5t40.5 -19t30.5 -19q14 0 21.5 12.5t11.5 48.5t4 103l-6 654q-1 201 46.5 305t138.5 104&#xA;q24 0 40 -13.5t16 -33.5z" /></g><g transform="matrix(.012,-0,0,-.012,6.687,22.988)"><path id="x3A9" d="M719 146l-18 -146h-243l-5 18q2 4 17 25t24 36l25 42t26.5 52.5t21 56.5t16 65t5.5 68q0 121 -55.5 194.5t-149.5 73.5q-95 0 -150 -72t-55 -199q0 -54 18.5 -114t36.5 -94t48.5 -82.5t32.5 -51.5l-7 -18h-244l-17 146l27 1q17 -49 31.5 -62t45.5 -13h89l-21 21t-26 26.5&#xA;l-26 29t-28 35.5l-23 37.5t-20.5 43t-12 45.5t-5.5 51q0 133 88 218.5t219 85.5q132 0 218 -83t86 -218q0 -40 -11.5 -78t-33 -71.5t-39 -56t-44 -51t-32.5 -35.5h84q35 0 48 12t31 63z" /></g><g transform="matrix(.017,-0,0,-.017,19.15,15.775)"><use xlink:href="#x1D454" /></g><g transform="matrix(.017,-0,0,-.017,28.822,15.775)"><path id="x1D462" d="M515 96q-37 -44 -84.5 -76t-71.5 -32q-12 0 -18 7t-6 34t10 75l19 89h-2q-87 -113 -181 -176q-43 -29 -83 -29q-46 0 -46 63q0 31 9 67l52 222q7 36 -1 36q-10 0 -76 -50l-13 24q47 45 92 71.5t67 26.5q18 0 21 -16.5t-8 -65.5l-56 -242q-16 -67 13 -67q41 0 114 74&#xA;t114 146l32 145l74 26h11q-52 -199 -80 -347q-8 -39 6 -39q7 0 32 17.5t47 39.5z" /></g><g transform="matrix(.012,-0,0,-.012,37.975,7.613)"><path id="x32" d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" /></g><g transform="matrix(.017,-0,0,-.017,49.025,15.775)"><path id="x2264" d="M531 71l-474 214v50l474 215v-56l-416 -184l416 -183v-56zM531 -40h-474v50h474v-50z" /></g><g transform="matrix(.017,-0,0,-.017,63.729,15.775)"><path id="x1D436" d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5&#xA;t325.5 101.5q114 0 204 -38z" /></g><g transform="matrix(.017,-0,0,-.017,78.535,15.775)"><use xlink:href="#x222B" /></g><g transform="matrix(.012,-0,0,-.012,85.175,22.988)"><use xlink:href="#x3A9" /></g><g transform="matrix(.017,-0,0,-.017,97.638,15.775)"><path id="x7C" d="M162 -163h-61v866h61v-866z" /></g><g transform="matrix(.017,-0,0,-.017,102.108,15.775)"><path id="x2207" d="M599 626l-268 -633l-28 -8l-261 641v24h557v-24zM535 600h-390l194 -489z" /></g><g transform="matrix(.017,-0,0,-.017,113.004,15.775)"><use xlink:href="#x1D462" /></g><g transform="matrix(.017,-0,0,-.017,122.15,15.775)"><use xlink:href="#x7C" /></g><g transform="matrix(.012,-0,0,-.012,126.625,7.613)"><use xlink:href="#x32" /></g><g transform="matrix(.017,-0,0,-.017,132.962,15.775)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g><g transform="matrix(.017,-0,0,-.017,145.321,15.775)"><use xlink:href="#x1D462" /></g><g transform="matrix(.017,-0,0,-.017,159.192,15.775)"><path id="x2208" d="M448 1h-83q-118 0 -201.5 74.5t-83.5 179.5t83.5 179.5t201.5 74.5h83v-50h-84q-87 0 -150.5 -51.5t-73.5 -127.5h308v-50h-308q10 -76 73.5 -127.5t150.5 -51.5h84v-50z" /></g><g transform="matrix(.017,-0,0,-.017,172.893,15.775)"><path id="x1D43B" d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28&#xA;h263l-6 -28q-58 -5 -75.5 -21t-30.5 -81l-26 -153h377l29 153q12 67 2 81t-74 21l5 28h268z" /></g><g transform="matrix(.012,-0,0,-.012,187.8,7.613)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g><g transform="matrix(.012,-0,0,-.012,187.8,19.863)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g><g transform="matrix(.017,-0,0,-.017,194.138,15.775)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,200.019,15.775)"><use xlink:href="#x3A9" /></g><g transform="matrix(.017,-0,0,-.017,212.887,15.775)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g></svg>, for some <svg style="vertical-align:-0.23206pt;width:39.6875px;" id="M3" height="11.75" version="1.1" viewBox="0 0 39.6875 11.75" width="39.6875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.4)"><use xlink:href="#x1D436" /></g><g transform="matrix(.017,-0,0,-.017,16.755,11.4)"><path id="x3E" d="M512 230l-437 -233v58l378 199v2l-378 200v58l437 -233v-51z" /></g><g transform="matrix(.017,-0,0,-.017,31.459,11.4)"><use xlink:href="#x30" /></g></svg>, where <svg style="vertical-align:-0.0pt;width:12.9875px;" id="M4" height="11.425" version="1.1" viewBox="0 0 12.9875 11.425" width="12.9875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.363)"><use xlink:href="#x3A9" /></g></svg> is a bounded domain in <svg style="vertical-align:-0.1092pt;width:19.049999px;" id="M5" height="15.975" version="1.1" viewBox="0 0 19.049999 15.975" width="19.049999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path id="x211D" d="M751 18q-1 -4 -2 -13t-2 -13q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -62 14 -77t74 -20v-28h-382v28q62 5 76 19.5t14 77.5v400q0 63 -14 77.5t-76 19.5v28h372q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172&#xA;q27 -52 89 -144q49 -71 81 -104q31 -36 72 -47zM543 469q0 76 -42 112t-104 36q-41 0 -54 -10q-11 -7 -11 -44v-247h48q73 0 108 29q55 42 55 124zM290 131v390q0 62 -7.5 79.5t-30.5 17.5q-24 0 -31.5 -17.5t-7.5 -79.5v-390q0 -62 7.5 -79.5t31.5 -17.5q23 0 30.5 17.5&#xA;t7.5 79.5z" /></g><g transform="matrix(.012,-0,0,-.012,12.663,7.613)"><use xlink:href="#x32" /></g></svg>. By making use of Muckenhoupt condition for the one-dimensional weighted Hardy inequalities, we identify a rearrangement invariant Banach function space so that the previous integral inequality holds for all weight functions in it. For weights in a subspace of this space, we show that the best constant in the previous inequality is attained. Our method gives an alternate way of proving the Moser-Trudinger embedding and its refinement due to Hansson.

T. V. Anoop

A Note on Generalized Hardy-Sobolev Inequalities

We prove a fixed point theorem for mappings satisfying an implicit relation in a complete fuzzy metric space.

Ismat Beg

Shaban Sedghi

Nabi Shobe

Fixed Point Theorems in Fuzzy Metric Spaces

This paper deals with the problem of stability analysis for singular systems with time-varying delay. By developing a delay decomposition approach, information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs), which can be easily solved by various optimization algorithms.  The merits of the proposed results lie in their less conservatism which is realized by choosing different Lyapunov matrices in the decomposed intervals and taking the information of the delayed plant states into full consideration. It is proved that the newly proposed criteria may introduce less conservatism than some existing ones. Meanwhile, the computational complexity of the presented stability criteria is reduced greatly since fewer decision variables are involved. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.

Pin-Lin Liu

Further Results on the Stability Analysis of Singular Systems with Time-Varying Delay: A Delay Decomposition Approach

We know from the classical sequence spaces theory that there is a useful relationship between continuous and <svg     style="vertical-align:-3.56265pt;width:10px;" id="M1" height="16.6625" version="1.1" viewBox="0 0 10 16.6625" width="10"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path id="x1D6FD" d="M558 587q0 -32 -14 -61t-40 -53.5t-48.5 -41t-54.5 -36.5q144 -51 144 -174q0 -55 -43.5 -108t-104.5 -87q-77 -42 -131 -42q-31 0 -54 20t-31 47l11 18q48 -29 108 -29q79 0 119.5 43t40.5 109t-44.5 107.5t-119.5 50.5l22 47q34 1 65 21q96 61 96 157q0 42 -24 67.5&#xA;t-62 25.5q-24 0 -43.5 -9t-35 -29.5t-27 -44t-22.5 -63t-19.5 -75.5t-18.5 -91q-57 -294 -68 -380q-26 -190 -35 -200q-26 -31 -97 -37l-4 26q19 9 48 170l77 413q23 121 52.5 187.5t83.5 114.5q70 62 148 62q51 0 88.5 -34t37.5 -91z" /></g>

		
	
</svg>-duals of a scalar-valued FK-space <svg     style="vertical-align:-0.0pt;width:10.8625px;" id="M2" height="11.175" version="1.1" viewBox="0 0 10.8625 11.175" width="10.8625"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x1D438" d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5&#xA;l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" /></g>

		
	
</svg> originated by the AK-property. Our main interest in this work is to expose relationships between the operator space <svg     style="vertical-align:-2.3205pt;width:56.962502px;" id="M3" height="15.0875" version="1.1" viewBox="0 0 56.962502 15.0875" width="56.962502"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x2112" d="M608 643l-12 -19q-56 33 -145 33q-87 0 -154 -42q-68 -42 -68 -115q0 -74 66 -116q67 -42 176 -42q21 0 63 5l29 56q34 66 57 103q43 65 106 113q65 50 122 50q41 0 62 -22t21 -60q0 -67 -87 -144q-88 -76 -217 -110q-46 -101 -119 -186q-72 -83 -136 -108&#xA;q71 -23 103 -23q141 0 265 139l19 -14q-131 -156 -281 -156q-84 0 -164 30q-70 -24 -155 -24q-126 0 -126 61q0 24 30 40.5t78 16.5q42 0 85 -16q18 -6 46 -18q26 -11 42 -16q41 26 99 98q58 70 105 158q-26 -3 -53 -3q-50 0 -96.5 10.5t-88.5 31.5t-67 60t-25 90&#xA;q0 78 73 130q74 53 182 53q98 0 165 -44zM890 588q0 44 -49 44q-55 0 -109 -80q-54 -81 -89 -183q46 12 104 45q64 35 103.5 81t39.5 93zM266 35v1q-73 43 -125 43q-67 0 -67 -25q0 -33 87 -33q65 0 105 14z" /></g><g transform="matrix(.017,-0,0,-.017,16.143,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,22.025,12.138)"><use xlink:href="#x1D438"/></g><g transform="matrix(.017,-0,0,-.017,32.768,12.138)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g><g transform="matrix(.017,-0,0,-.017,39.466,12.138)"><path id="x1D44C" d="M667 650l-9 -28q-53 -5 -76 -17t-64 -59q-51 -61 -175 -225q-21 -29 -27 -55l-27 -136q-13 -65 -0.5 -80t83.5 -22l-7 -28h-280l8 28q64 4 81 19t30 83l25 128q6 35 -7 65l-98 231q-17 41 -32.5 52t-68.5 16l8 28h252l-6 -28l-40 -4q-27 -3 -33 -12.5t2 -31.5&#xA;q8 -26 43 -107.5t61 -134.5q114 145 174 240q14 24 8 33t-37 13l-34 4l8 28h238z" /></g><g transform="matrix(.017,-0,0,-.017,51.008,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g>

		
	
</svg> and <svg     style="vertical-align:-0.0pt;width:18.4px;" id="M4" height="16.75" version="1.1" viewBox="0 0 18.4 16.75" width="18.4"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,16.7)"><use xlink:href="#x1D438"/></g>

			<g transform="matrix(.012,-0,0,-.012,10.8,8.538)"><use xlink:href="#x1D6FD"/></g>

		
	
</svg> and the generalized <svg     style="vertical-align:-3.56265pt;width:10px;" id="M5" height="16.6625" version="1.1" viewBox="0 0 10 16.6625" width="10"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D6FD"/></g>

		
	
</svg>-duals of some <svg     style="vertical-align:-0.0pt;width:13.5875px;" id="M6" height="11.175" version="1.1" viewBox="0 0 13.5875 11.175" width="13.5875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x1D44B" d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231&#xA;l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" /></g>

		
	
</svg>-valued AK-space <svg     style="vertical-align:-0.0pt;width:10.8625px;" id="M7" height="11.175" version="1.1" viewBox="0 0 10.8625 11.175" width="10.8625"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D438"/></g>

		
	
</svg> where <svg     style="vertical-align:-0.0pt;width:13.5875px;" id="M8" height="11.175" version="1.1" viewBox="0 0 13.5875 11.175" width="13.5875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D44B"/></g>

		
	
</svg> and <svg     style="vertical-align:-0.0pt;width:11.6625px;" id="M9" height="11.175" version="1.1" viewBox="0 0 11.6625 11.175" width="11.6625"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D44C"/></g>

		
	
</svg> are Banach spaces and <svg     style="vertical-align:-3.71138pt;width:471.35001px;" id="M10" height="21.375" version="1.1" viewBox="0 0 471.35001 21.375" width="471.35001"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,16.7)"><use xlink:href="#x1D438"/></g>

			<g transform="matrix(.012,-0,0,-.012,10.8,8.537)"><use xlink:href="#x1D6FD"/></g>

			<g transform="matrix(.017,-0,0,-.017,23.063,16.7)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,37.749,16.7)"><path id="x7B" d="M293 -169q-145 0 -145 128q0 35 4 106t3 104q0 17 -2 28t-10 25.5t-28 23t-51 10.5v29q31 2 51 10.5t28 23t10 25.5t2 28q0 31 -4 101t-3 104q0 132 145 132v-28q-51 -7 -67.5 -30t-16.5 -63q0 -32 6.5 -99.5t6.5 -100.5q0 -97 -83 -115v-4q83 -20 83 -117&#xA;q0 -34 -6.5 -99.5t-6.5 -96.5q0 -41 16.5 -65.5t67.5 -31.5v-28z" /></g><g transform="matrix(.017,-0,0,-.017,43.648,16.7)"><use xlink:href="#x28"/></g><g transform="matrix(.017,-0,0,-.017,49.53,16.7)"><path id="x1D434" d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" /></g>

			<g transform="matrix(.012,-0,0,-.012,62,20.775)"><path id="x1D458" d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1&#xA;l5 26q38 4 74 13.5t57 17t25 7.5q12 0 4 -32l-104 -443h2q35 38 97 93q39 35 65.5 56t62 41.5t58.5 20.5q19 0 30.5 -10t11.5 -22z" /></g>

			<g transform="matrix(.017,-0,0,-.017,68.612,16.7)"><use xlink:href="#x29"/></g><g transform="matrix(.017,-0,0,-.017,74.494,16.7)"><use xlink:href="#x2C"/></g><g transform="matrix(.017,-0,0,-.017,81.192,16.7)"><use xlink:href="#x1D434"/></g>

			<g transform="matrix(.012,-0,0,-.012,93.663,20.775)"><use xlink:href="#x1D458"/></g>

			<g transform="matrix(.017,-0,0,-.017,104.988,16.7)"><path id="x2208" d="M448 1h-83q-118 0 -201.5 74.5t-83.5 179.5t83.5 179.5t201.5 74.5h83v-50h-84q-87 0 -150.5 -51.5t-73.5 -127.5h308v-50h-308q10 -76 73.5 -127.5t150.5 -51.5h84v-50z" /></g><g transform="matrix(.017,-0,0,-.017,118.688,16.7)"><use xlink:href="#x2112"/></g><g transform="matrix(.017,-0,0,-.017,134.769,16.7)"><use xlink:href="#x28"/></g><g transform="matrix(.017,-0,0,-.017,140.651,16.7)"><use xlink:href="#x1D44B"/></g><g transform="matrix(.017,-0,0,-.017,154.114,16.7)"><use xlink:href="#x2C"/></g><g transform="matrix(.017,-0,0,-.017,160.811,16.7)"><use xlink:href="#x1D44C"/></g><g transform="matrix(.017,-0,0,-.017,172.354,16.7)"><use xlink:href="#x29"/></g><g transform="matrix(.017,-0,0,-.017,182.961,16.7)"><path id="x2236" d="M223 355q0 -25 -15.5 -41.5t-39.5 -16.5t-40 16.5t-16 41.5t16 41t40 16t39.5 -16t15.5 -41zM223 46q0 -26 -16 -42t-40 -16t-39.5 16t-15.5 42q0 24 16 40.5t39 16.5q24 0 40 -16.5t16 -40.5z" /></g><g transform="matrix(.017,-0,0,-.017,193.364,16.7)"><path id="x2211" d="M697 -46l-42 -182h-602v25l325 457l-308 460v25h585l12 -154l-28 -5q-17 63 -39 88q-12 15 -36.5 20.5t-80.5 5.5h-277l268 -396l-311 -440h382q51 0 75.5 19.5t47.5 83.5z" /></g>

			<g transform="matrix(.012,-0,0,-.012,206.112,8.425)"><path id="x221E" d="M983 225q0 -112 -67 -174.5t-150 -62.5q-91 0 -154.5 43.5t-113.5 129.5q-49 -85 -104 -129t-138 -44q-98 0 -158.5 66t-60.5 154q0 59 21 106.5t54.5 75.5t70.5 43t73 15q90 0 152.5 -43.5t112.5 -128.5q48 84 104.5 128t140.5 44q93 0 155 -65t62 -158zM478 196&#xA;q-27 49 -47 80t-50 67t-64 54t-73 18q-48 0 -81.5 -47t-33.5 -128q0 -96 37.5 -157.5t99.5 -61.5q68 0 117.5 47t94.5 128zM889 204q0 91 -35.5 151t-99.5 60q-68 0 -119 -47t-95 -127q27 -49 47 -80.5t50 -67.5t65 -54t74 -18q113 0 113 183z" /></g><g transform="matrix(.012,-0,0,-.012,206.112,21.175)"><use xlink:href="#x1D458"/></g><g transform="matrix(.012,-0,0,-.012,212.098,21.175)"><use xlink:href="#x3D"/></g><g transform="matrix(.012,-0,0,-.012,219.082,21.175)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g>

			<g transform="matrix(.017,-0,0,-.017,228.25,16.7)"><use xlink:href="#x1D434"/></g>

			<g transform="matrix(.012,-0,0,-.012,240.712,20.775)"><use xlink:href="#x1D458"/></g>

			<g transform="matrix(.017,-0,0,-.017,247.325,16.7)"><path id="x1D465" d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37&#xA;q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" /></g>

			<g transform="matrix(.012,-0,0,-.012,256.825,20.775)"><use xlink:href="#x1D458"/></g>

			<g transform="matrix(.017,-0,0,-.017,269.1,16.7)"><path id="x63" d="M390 111l17 -21q-34 -45 -80 -73.5t-89 -28.5q-91 0 -146 62t-55 147q0 118 101 195q74 57 149 57h1q59 0 90 -27q16 -14 16 -30q0 -15 -12 -29t-21 -14q-8 0 -19 11q-44 41 -101 41q-52 0 -87.5 -42.5t-35.5 -117.5q0 -49 15 -87t39 -58t49 -30t48 -10q33 0 60.5 12&#xA;t60.5 43z" /></g><g transform="matrix(.017,-0,0,-.017,276.29,16.7)"><path id="x6F" d="M257 449q92 0 154 -65t62 -158q0 -112 -67 -175t-150 -63q-98 0 -158.5 66.5t-60.5 154.5q0 59 21 106.5t54.5 75.5t71 43t73.5 15zM244 416q-48 0 -81 -47t-33 -128q0 -96 38 -158t99 -62q51 0 82 43.5t31 139.5q0 91 -36 151.5t-100 60.5z" /></g><g transform="matrix(.017,-0,0,-.017,284.756,16.7)"><path id="x6E" d="M524 0h-209v26q44 5 55 18t11 65v167q0 114 -91 114q-50 0 -109 -51v-235q0 -50 10 -61.5t55 -16.5v-26h-217v26q51 5 62 17t11 61v206q0 47 -9.5 58.5t-50.5 19.5v23q82 15 139 40v-79l67 47q47 30 83 30q60 0 94.5 -40t34.5 -112v-193q0 -50 10 -61.5t54 -16.5v-26z&#xA;" /></g><g transform="matrix(.017,-0,0,-.017,293.663,16.7)"><path id="x76" d="M478 437v-26q-39 -5 -53 -17.5t-35 -57.5q-68 -149 -142 -347h-28q-47 128 -138 350q-17 43 -30.5 54.5t-53.5 17.5v26h205v-26q-40 -4 -46.5 -14.5t6.5 -42.5q41 -115 95 -247q43 101 89 238q12 36 3.5 48.5t-50.5 17.5v26h178z" /></g><g transform="matrix(.017,-0,0,-.017,301.398,16.7)"><path id="x65" d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3&#xA;q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" /></g><g transform="matrix(.017,-0,0,-.017,308.622,16.7)"><path id="x72" d="M181 342h2q63 107 121 107q24 0 41 -16t17 -34q0 -34 -32 -49q-17 -7 -26 2q-21 20 -43 20q-20 0 -42 -22t-38 -63v-183q0 -50 12.5 -62t69.5 -16v-26h-230v26q47 5 58 17t11 61v207q0 49 -9 60.5t-53 16.5v23q74 12 141 40v-109z" /></g><g transform="matrix(.017,-0,0,-.017,314.793,16.7)"><path id="x67" d="M463 437l5 -8q-21 -38 -45 -51l-57 3q30 -35 30 -88q0 -76 -52.5 -118t-122.5 -42q-24 0 -51 5q-30 -21 -30 -42q0 -16 16 -27t47 -11q19 0 54 0.5t52 0.5q36 0 65.5 -8t53.5 -36t24 -74q0 -77 -75 -137.5t-174 -60.5q-79 0 -126 37.5t-48 84.5q0 32 24 56q21 21 83 70&#xA;q-49 15 -74 55q-13 20 -11 42q56 21 88 61q-37 16 -62.5 51t-25.5 83q0 78 56.5 122t122.5 44h1q51 0 96 -27q71 4 136 15zM219 418q-34 0 -58 -32t-24 -87q0 -59 26.5 -96.5t67.5 -37.5q35 1 59 32t24 87q0 59 -26 96.5t-69 37.5zM241 -11q-62 0 -87 -21q-46 -39 -46 -78&#xA;q0 -41 38 -68.5t94 -27.5q69 0 106.5 31t37.5 80q0 52 -45 71q-33 13 -98 13z" /></g><g transform="matrix(.017,-0,0,-.017,322.612,16.7)"><use xlink:href="#x65"/></g><g transform="matrix(.017,-0,0,-.017,329.837,16.7)"><path id="x73" d="M319 325l-25 -7q-33 99 -103 99q-29 0 -47 -19.5t-18 -49.5t22 -49.5t62 -36.5q63 -26 95 -57t32 -79q0 -64 -50 -101t-115 -37q-35 0 -67.5 10.5t-46.5 23.5q-5 11 -11 51t-6 67l27 5q14 -53 46.5 -88.5t75.5 -35.5q29 0 50 19.5t21 50.5t-19.5 51.5t-59.5 39.5&#xA;q-28 12 -46 22.5t-38.5 27t-30.5 38.5t-10 49q0 54 42.5 92t109.5 38q48 0 88 -18q6 -15 13 -50.5t9 -55.5z" /></g><g transform="matrix(.017,-0,0,-.017,341.736,16.7)"><path id="x69" d="M135 536q-20 0 -35 15.5t-15 35.5q0 22 15 37t36 15t35.5 -15t14.5 -37q0 -21 -15 -36t-36 -15zM252 0h-220v26q48 5 59 17t11 63v206q0 47 -9 58t-54 18v24q78 12 142 39v-345q0 -51 11.5 -63t59.5 -17v-26z" /></g><g transform="matrix(.017,-0,0,-.017,346.291,16.7)"><use xlink:href="#x6E"/></g><g transform="matrix(.017,-0,0,-.017,361.25,16.7)"><use xlink:href="#x1D44C"/></g><g transform="matrix(.017,-0,0,-.017,372.792,16.7)"><use xlink:href="#x2C"/></g><g transform="matrix(.017,-0,0,-.017,379.507,16.7)"><path id="x66" d="M54 437h47v21q0 48 11 83q23 72 77 118q55 46 110 53q53 -3 79 -34q13 -16 5 -35q-5 -13 -19 -24t-27 3q-37 37 -81 37q-34 0 -53 -29q-24 -37 -23 -153v-40h118q5 -7 1.5 -21t-11.5 -19h-108v-287q0 -55 13 -67t73 -18v-25h-236v26q49 5 60 16.5t11 60.5v294h-70l-4 11z&#xA;" /></g><g transform="matrix(.017,-0,0,-.017,384.403,16.7)"><use xlink:href="#x6F"/></g><g transform="matrix(.017,-0,0,-.017,392.868,16.7)"><use xlink:href="#x72"/></g><g transform="matrix(.017,-0,0,-.017,404.818,16.7)"><path id="x61" d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5&#xA;t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" /></g><g transform="matrix(.017,-0,0,-.017,412.365,16.7)"><path id="x6C" d="M238 0h-223v26q48 5 60 17t12 61v473q0 50 -10.5 60.5t-58.5 15.5v24q73 8 148 35v-608q0 -49 11.5 -61t60.5 -17v-26z" /></g><g transform="matrix(.017,-0,0,-.017,416.751,16.7)"><use xlink:href="#x6C"/></g><g transform="matrix(.017,-0,0,-.017,426.712,16.7)"><use xlink:href="#x1D465"/></g><g transform="matrix(.017,-0,0,-.017,440.94,16.7)"><use xlink:href="#x2208"/></g><g transform="matrix(.017,-0,0,-.017,454.641,16.7)"><use xlink:href="#x1D438"/></g><g transform="matrix(.017,-0,0,-.017,465.385,16.7)"><path id="x7D" d="M283 255q-31 -2 -51 -10.5t-28 -23.5t-10 -27t-2 -30q0 -28 4 -97.5t4 -107.5q0 -128 -146 -128v28q50 7 67.5 31t17.5 63q0 33 -7 100t-7 98q0 96 84 117v4q-84 20 -84 115q0 34 7 102.5t7 98.5q0 40 -17.5 63t-67.5 30v28q28 0 50 -4t45.5 -16.5t37 -40t13.5 -68.5&#xA;q0 -37 -4 -106.5t-4 -98.5q0 -18 2 -30t10 -27t28 -23.5t51 -10.5v-29z" /></g>

		
	
</svg>. Further, by these results, we obtain the generalized <svg     style="vertical-align:-3.56265pt;width:10px;" id="M11" height="16.6625" version="1.1" viewBox="0 0 10 16.6625" width="10"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D6FD"/></g>

		
	
</svg>-duals of some vector-valued Orlicz sequence spaces.

Y&#x131;lmaz Y&#x131;lmaz

Generalized K&#xf6;the-Toeplitz Duals of Some Vector-Valued Sequence Spaces

About this journal

Journal profile

Meet the editorial board

Editor spotlight

Find out more

This journal's articles appear in a wide range of abstracting and indexing databases, and are covered by numerous other services that aid discovery and access. Find out more about where and how the content of this journal is available.

International Journal of Analysis