Journal of Function Spaces https://www.hindawi.com The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. A Subclass of Analytic Functions Related to -Uniformly Convex and Starlike Functions Tue, 23 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/9010964/ We investigate some subclasses of -uniformly convex and -uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed. Saqib Hussain, Akhter Rasheed, Muhammad Asad Zaighum, and Maslina Darus Copyright © 2017 Saqib Hussain et al. All rights reserved. Approximation of Functions on a Square by Interpolation Polynomials at Vertices and Few Fourier Coefficients Mon, 22 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/9376505/ For a bivariate function on a square, in general, its Fourier coefficients decay slowly, so one cannot reconstruct it by few Fourier coefficients. In this paper we will develop a new approximation scheme to overcome the weakness of Fourier approximation. In detail, we will use Lagrange interpolation and linear interpolation on the boundary of the square to derive a new approximation scheme such that we can use the values of the target function at vertices of the square and few Fourier coefficients to reconstruct the target function with very small error. Zhihua Zhang Copyright © 2017 Zhihua Zhang. All rights reserved. A Note on Reducing Subspaces of Toeplitz Operator on the Weighted Analytic Function Spaces of the Bidisk Sun, 07 May 2017 09:03:44 +0000 http://www.hindawi.com/journals/jfs/2017/5807909/ We discussed the reducing subspaces of Toeplitz operators on the weighted analytic function spaces of bidisk . The result shows that if the weight is of type-I, the structure of reducing subspaces of on is very simple. Hongzhao Lin Copyright © 2017 Hongzhao Lin. All rights reserved. A New Subclass of -Janowski Type Functions Associated with Ruscheweyh Derivative Wed, 03 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/6095293/ We introduce and investigate a new subclass of analytic functions using Ruscheweyh derivative. We derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the general class, which we have introduced and studied in this article. We also observe that this class is preserved under the Bernardi integral transform. Shahid Mahmood, Sarfraz Nawaz Malik, Saima Mustafa, and S. M. Jawwad Riaz Copyright © 2017 Shahid Mahmood et al. All rights reserved. The Embedding Theorem of an -Prebarreled Module into Its Random Biconjugate Space Sun, 30 Apr 2017 07:49:50 +0000 http://www.hindawi.com/journals/jfs/2017/8520797/ We first prove Mazur’s lemma in a random locally convex module endowed with the locally -convex topology. Then, we establish the embedding theorem of an -prebarreled random locally convex module, which says that if is an -prebarreled random locally convex module such that has the countable concatenation property, then the canonical embedding mapping of onto is an -linear homeomorphism, where is the strong random biconjugate space of under the locally -convex topology. Xia Zhang and Ming Liu Copyright © 2017 Xia Zhang and Ming Liu. All rights reserved. Existence and Multiplicity of Positive Solutions for Schrödinger-Kirchhoff-Poisson System with Singularity Sun, 23 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/5985962/ We study a singular Schrödinger-Kirchhoff-Poisson system by the variational methods and the Nehari manifold and we prove the existence, uniqueness, and multiplicity of positive solutions of the problem under different conditions. Mengjun Mu and Huiqin Lu Copyright © 2017 Mengjun Mu and Huiqin Lu. All rights reserved. Redefinition of -Distance in Metric Spaces Thu, 20 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/4168486/ The concept of -distance was introduced in 2001; on the other hand, that of -function was introduced by Lin and Du. Strongly inspired by -function, we introduce a new concept, which is a very slight generalization of -distance and is more natural than -distance. So we could say that we redefine -distance in some sense. Tomonari Suzuki Copyright © 2017 Tomonari Suzuki. All rights reserved. Distortion Type Theorems for Functions in the Logarithmic Bloch Space Sun, 16 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/8694516/ We establish distortion type theorems for locally schlicht functions and for functions having branch points satisfying a normalized Bloch condition in the closed unit ball of the logarithmic Bloch space . As a consequence of our results we have estimations of the schlicht radius for functions in these classes. Armando J. García-Ortíz, Milton del Castillo Lesmes Acosta, and Julio C. Ramos-Fernández Copyright © 2017 Armando J. García-Ortíz et al. All rights reserved. Commuting Toeplitz and Hankel Operators on Harmonic Dirichlet Spaces Thu, 13 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/9627109/ On the harmonic Dirichlet space of the unit disk, the commutativity of Toeplitz and Hankel operators is studied. We obtain characterizations of commuting Toeplitz and Hankel operators and essentially commuting (semicommuting) Toeplitz and Hankel operators with general symbols. Qian Ding, Yong Chen, and Yufeng Lu Copyright © 2017 Qian Ding et al. All rights reserved. On Similarity and Reducing Subspaces of the -Shift plus Certain Weighted Volterra Operator Thu, 13 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/8370139/ Let be an -degree polynomial . Inspired by Sarason’s result, we introduce the operator defined by the multiplication operator plus the weighted Volterra operator on the Bergman space. We show that the operator is similar to on some Hilbert space . Then for , by using matrix manipulations, the reducing subspaces of the corresponding operator on the Bergman space are characterized. Yucheng Li, Hao Chen, and Wenhua Lan Copyright © 2017 Yucheng Li et al. All rights reserved. Essential Norms of Volterra Type Operators between Zygmund Type Spaces Tue, 11 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/1409642/ We investigate the boundedness of some Volterra type operators between Zygmund type spaces. Then, we give the essential norms of such operators in terms of , their derivatives, and the nth power of . Shanli Ye and Caishu Lin Copyright © 2017 Shanli Ye and Caishu Lin. All rights reserved. Global Attractors of the Extensible Plate Equations with Nonlinear Damping and Memory Tue, 04 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/4896161/ We prove in this paper the existence of a global attractor for the plate equations of Kirchhoff type with nonlinear damping and memory using the contraction function method. Xiaobin Yao and Qiaozhen Ma Copyright © 2017 Xiaobin Yao and Qiaozhen Ma. All rights reserved. Toeplitz Operators, Pseudo-Homogeneous Symbols, and Moment Maps on the Complex Projective Space Mon, 03 Apr 2017 07:19:41 +0000 http://www.hindawi.com/journals/jfs/2017/1730920/ Following previous works for the unit ball due to Nikolai Vasilevski, we define quasi-radial pseudo-homogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplitz operators. A geometric interpretation of these symbols in terms of moment maps is developed. This leads us to the introduction of a new family of symbols, extended pseudo-homogeneous, that provide larger commutative Banach algebras generated by Toeplitz operators. This family of symbols provides new commutative Banach algebras generated by Toeplitz operators on the unit ball. Miguel Antonio Morales-Ramos, Raul Quiroga-Barranco, and Armando Sanchez-Nungaray Copyright © 2017 Miguel Antonio Morales-Ramos et al. All rights reserved. Some New Fixed Point Theorems in Partial Metric Spaces with Applications Wed, 29 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/1072750/ Recently, a number of fixed point theorems for contraction type mappings in partial metric spaces have been obtained by various authors. Most of these theorems can be obtained from the corresponding results in metric spaces. The purpose of this paper is to present certain fixed point results for single and multivalued mappings in partial metric spaces which cannot be obtained from the corresponding results in metric spaces. Besides discussing some useful examples, an application to Volterra type system of integral equations is also discussed. Rajendra Pant, Rahul Shukla, H. K. Nashine, and R. Panicker Copyright © 2017 Rajendra Pant et al. All rights reserved. Function Spaces, Fixed Points, Approximations, and Applications Mon, 27 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/2074917/ Giuseppe Marino, Filomena Cianciaruso, Nawab Hussain, and Enrique Llorens Fuster Copyright © 2017 Giuseppe Marino et al. All rights reserved. Statistical -Convergence in Probabilistic Normed Spaces Sun, 19 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/3154280/ The main objective of the study was to understand the notion of Λ-convergence and to study the notion of probabilistic normed spaces. The study has also aimed to define the statistical Λ-convergence and statistical Λ-Cauchy in PN-spaces. The concepts of these approaches have been defined by some examples, which have demonstrated the concepts of statistical Λ-convergence and statistical Λ-Cauchy in PN-spaces. Previous studies have also been used to understand similar terminologies and notations for the extraction of outcomes. M. Aldhaifallah, K. S. Nisar, H. M. Srivastava, and M. Mursaleen Copyright © 2017 M. Aldhaifallah et al. All rights reserved. A KAM Theorem for Lower Dimensional Elliptic Invariant Tori of Nearly Integrable Symplectic Mappings Thu, 16 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/3719395/ This paper develops a new KAM theorem for a class of lower dimensional elliptic invariant tori of nearly integrable symplectic mappings with generating functions but without assuming any nondegenerate condition. Shunjun Jiang Copyright © 2017 Shunjun Jiang. All rights reserved. Comment on “On the Frame Properties of Degenerate System of Sines” Wed, 15 Mar 2017 09:27:36 +0000 http://www.hindawi.com/journals/jfs/2017/9257076/ The proof of Theorem 3.1 of the paper “On the Frame Properties of Degenerate System of Sines” (see (Bilalov and Guliyeva, 2012)) published earlier in this journal contains a gap; the reasoning given there to prove this theorem is not enough to state the validity of the mentioned theorem. To overcome this shortage we state the most general fact on the completeness of sine system which implies in particular the validity of this fact. It is shown in this note that the system , where is an exponential or trigonometric (cosine or sine) systems, becomes complete in the corresponding Lebesgue space or , respectively, whenever belongs to the corresponding Lebesgue space for all indices (under the evident natural condition ). It is also shown that the same conclusion does not remain valid for, in general, any complete or complete orthonormal system . Besides it, the largest class of functions for which the system is complete in space is determined. Aydin Sh. Shukurov Copyright © 2017 Aydin Sh. Shukurov. All rights reserved. Global Hölder Estimates via Morrey Norms for Hypoelliptic Operators with Drift Sun, 19 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/2805457/ Suppose that are left invariant real vector fields on the homogeneous group with being homogeneous of degree two and homogeneous of degree one. In the paper we study the hypoelliptic operator with drift of the kind where and is a constant matrix satisfying the elliptic condition on . By proving the boundedness of two integral operators on the Morrey spaces with two weights, we obtain global Hölder estimates for . Yuexia Hou and Pengcheng Niu Copyright © 2017 Yuexia Hou and Pengcheng Niu. All rights reserved. Fixed Point Theorems for Manageable Contractions with Application to Integral Equations Thu, 16 Feb 2017 07:40:56 +0000 http://www.hindawi.com/journals/jfs/2017/7943896/ In this paper we utilize the concept of manageable functions to define multivalued manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations. N. Hussain, I. Iqbal, Badriah A. S. Alamri, and M. A. Kutbi Copyright © 2017 N. Hussain et al. All rights reserved. New Approach for Common Fixed Point Theorems via -Class Functions in -Metric Spaces Thu, 16 Feb 2017 07:40:10 +0000 http://www.hindawi.com/journals/jfs/2017/2624569/ We prove a new approach for some common fixed point results in complete -metric spaces for weakly increasing self-mappings satisfying -contractions via the concept of -class functions. An example is also provided. A. H. Ansari, M. A. Barakat, and H. Aydi Copyright © 2017 A. H. Ansari et al. All rights reserved. Boundedness of Fractional Oscillatory Integral Operators and Their Commutators in Vanishing Generalized Weighted Morrey Spaces Thu, 16 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/3295376/ In this article, we give the boundedness conditions in terms of Zygmund-type integral inequalities for oscillatory integral operators and fractional oscillatory integral operators on the vanishing generalized weighted Morrey spaces. Moreover, we investigate corresponding commutators. Bilal Çekiç and Ayşegül Çelik Alabalık Copyright © 2017 Bilal Çekiç and Ayşegül Çelik Alabalık. All rights reserved. General Holmstedt’s Formulae for the -Functional Tue, 14 Feb 2017 06:15:16 +0000 http://www.hindawi.com/journals/jfs/2017/4958073/ Explicit formulae for the -functional for the general couple , where is a compatible couple of quasi-normed spaces, are proved. As a consequence, the corresponding reiteration theorems are derived. Irshaad Ahmed, Georgi E. Karadzhov, and Ali Raza Copyright © 2017 Irshaad Ahmed et al. All rights reserved. On Harmonically -Preinvex Functions Tue, 31 Jan 2017 09:09:19 +0000 http://www.hindawi.com/journals/jfs/2017/2148529/ We define a new generalized class of harmonically preinvex functions named harmonically -preinvex functions, which includes harmonic -preinvex functions, harmonic -preinvex functions, harmonic -preinvex functions, and -convex functions as special cases. We also investigate the properties and characterizations of harmonically -preinvex functions. Finally, we establish some integral inequalities to show the applications of harmonically -preinvex functions. Shan-He Wu, Imran Abbas Baloch, and İmdat İşcan Copyright © 2017 Shan-He Wu et al. All rights reserved. Fixed Point Theorems for Multivalued Nonself -Almost Contractions in Banach Spaces Endowed with Graphs Tue, 31 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/7053849/ In this paper, we prove some fixed point theorems for multivalued nonself -almost contractions in Banach spaces with a directed graph and give some examples to illustrate our main results. The main results in this paper extend and generalize many known results in the literature therein. J. Tiammee, P. Charoensawan, and S. Suantai Copyright © 2017 J. Tiammee et al. All rights reserved. Iterative Schemes for Nonconvex Quasi-Variational Problems with -Prox-Regular Data in Banach Spaces Mon, 30 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/8708065/ In this paper, we propose an extension of quasi-equilibrium problems from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. The proposed problem is called quasi-variational problem. We study the convergence of some algorithms to solutions of the proposed nonconvex problems in Banach spaces. M. Bounkhel and Dj. Bounekhel Copyright © 2017 M. Bounkhel and Dj. Bounekhel. All rights reserved. Boundedness of the Segal-Bargmann Transform on Fractional Hermite-Sobolev Spaces Thu, 19 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/9176914/ Let and . We prove that the Segal-Bargmann transform is a bounded operator from fractional Hermite-Sobolev spaces to fractional Fock-Sobolev spaces . Hong Rae Cho, Hyunil Choi, and Han-Wool Lee Copyright © 2017 Hong Rae Cho et al. All rights reserved. Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative Tue, 17 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2017/5739196/ In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases. Xiaofei Li, Deng Ding, Liping Xu, Chuan Qin, and Songbo Hu Copyright © 2017 Xiaofei Li et al. All rights reserved. Boundedness for Commutators of Bilinear -Type Calderón-Zygmund Operators on Nonhomogeneous Metric Measure Spaces Mon, 09 Jan 2017 09:29:28 +0000 http://www.hindawi.com/journals/jfs/2017/3690452/ Let be a nonhomogeneous metric measure space. In this paper, the boundedness for commutators generated by bilinear -type Calderón-Zygmund operators and functions on is obtained. Rulong Xie, Lisheng Shu, and Aiwen Sun Copyright © 2017 Rulong Xie et al. All rights reserved. A -Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions Mon, 02 Jan 2017 06:46:55 +0000 http://www.hindawi.com/journals/jfs/2017/5309698/ In this paper, we apply the -algorithm to solve the constrained minimization problem of a maximum eigenvalue function which is the composite function of an affine matrix-valued mapping and its maximum eigenvalue. Here, we convert the constrained problem into its equivalent unconstrained problem by the exact penalty function. However, the equivalent problem involves the sum of two nonsmooth functions, which makes it difficult to apply -algorithm to get the solution of the problem. Hence, our strategy first applies the smooth convex approximation of maximum eigenvalue function to get the approximate problem of the equivalent problem. Then the approximate problem, the space decomposition, and the -Lagrangian of the object function at a given point will be addressed particularly. Finally, the -algorithm will be presented to get the approximate solution of the primal problem by solving the approximate problem. Wei Wang, Ming Jin, Shanghua Li, and Xinyu Cao Copyright © 2017 Wei Wang et al. All rights reserved.