Abstract and Applied Analysis https://www.hindawi.com The latest articles from Hindawi © 2018 , Hindawi Limited . All rights reserved. Necessary and Sufficient Conditions for Set-Valued Maps with Set Optimization Mon, 01 Jan 2018 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2018/5962049/ Optimality conditions are studied for set-valued maps with set optimization. Necessary conditions are given in terms of -derivative and contingent derivative. Sufficient conditions for the existence of solutions are shown for set-valued maps under generalized quasiconvexity assumptions. Abdessamad Oussarhan and Ikram Daidai Copyright © 2018 Abdessamad Oussarhan and Ikram Daidai. All rights reserved. Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity Mon, 01 Jan 2018 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2018/8325919/ In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons. Anwar Ja’afar Mohamad Jawad and Mahmood Jawad Abu-AlShaeer Copyright © 2018 Anwar Ja’afar Mohamad Jawad and Mahmood Jawad Abu-AlShaeer. All rights reserved. Contractibility of Fixed Point Sets of Mean-Type Mappings Sun, 31 Dec 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/3689069/ We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by Matkowski to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting. S. Iampiboonvatana and P. Chaoha Copyright © 2017 S. Iampiboonvatana and P. Chaoha. All rights reserved. Finite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systems Sun, 24 Dec 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/3273480/ Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS-) based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP) solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions. Xiaoxing Chen and Manfeng Hu Copyright © 2017 Xiaoxing Chen and Manfeng Hu. All rights reserved. First Passage Time of a Markov Chain That Converges to Bessel Process Sun, 03 Dec 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/7189826/ We investigate the probability of the first hitting time of some discrete Markov chain that converges weakly to the Bessel process. Both the probability that the chain will hit a given boundary before the other and the average number of transitions are computed explicitly. Furthermore, we show that the quantities that we obtained tend (with the Euclidian metric) to the corresponding ones for the Bessel process. Moussa Kounta Copyright © 2017 Moussa Kounta. All rights reserved. Approximation Properties of -Bernoulli Polynomials Sun, 03 Dec 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/9828065/ We study the -analogue of Euler-Maclaurin formula and by introducing a new -operator we drive to this form. Moreover, approximation properties of -Bernoulli polynomials are discussed. We estimate the suitable functions as a combination of truncated series of -Bernoulli polynomials and the error is calculated. This paper can be helpful in two different branches: first we solve the differential equations by estimating functions and second we may apply these techniques for operator theory. M. Momenzadeh and I. Y. Kakangi Copyright © 2017 M. Momenzadeh and I. Y. Kakangi. All rights reserved. Corrigendum to “A Three-Point Boundary Value Problem with an Integral Condition for a Third-Order Partial Differential Equation” Sun, 26 Nov 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/8604153/ C. Latrous and A. Memou Copyright © 2017 C. Latrous and A. Memou. All rights reserved. On the Output Controllability of Positive Discrete Linear Delay Systems Thu, 23 Nov 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/3651271/ Necessary and sufficient conditions for output reachability and null output controllability of positive linear discrete systems with delays in state, input, and output are established. It is also shown that output reachability and null output controllability together imply output controllability. Mouhcine Naim, Fouad Lahmidi, Abdelwahed Namir, and Mostafa Rachik Copyright © 2017 Mouhcine Naim et al. All rights reserved. Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function Wed, 22 Nov 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/1364914/ We introduce a generalized sigmoidal transformation on a given interval with a threshold at . Using , we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by some numerical examples. Beong In Yun Copyright © 2017 Beong In Yun. All rights reserved. Corrigendum to “Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems” Thu, 02 Nov 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/2739102/ Teffera M. Asfaw Copyright © 2017 Teffera M. Asfaw. All rights reserved. Applications of the -Drazin Inverse to the Heat Equation and a Delay Differential Equation Wed, 01 Nov 2017 10:01:50 +0000 http://www.hindawi.com/journals/aaa/2017/4248304/ We consider applications of the -Drazin inverse to some classes of abstract Cauchy problems, namely, the heat equation with operator coefficient and delay differential equations in Banach space. Alrazi Abdeljabbar and Trung Dinh Tran Copyright © 2017 Alrazi Abdeljabbar and Trung Dinh Tran. All rights reserved. The Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Prices Wed, 18 Oct 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/3286549/ In this paper, we analyze the role of the jump size distribution in the US natural gas prices when valuing natural gas futures traded at New York Mercantile Exchange (NYMEX) and we observe that a jump-diffusion model always provides lower errors than a diffusion model. Moreover, we also show that although the Normal distribution offers lower errors for short maturities, the Exponential distribution is quite accurate for long maturities. We also price natural gas options and we see that, in general, the model with the Normal jump size distribution underprices these options with respect to the Exponential distribution. Finally, we obtain the futures risk premia in both cases and we observe that for long maturities the term structure of the risk premia is negative. Moreover, the Exponential distribution provides the highest premia in absolute value. L. Gómez-Valle, Z. Habibilashkary, and J. Martínez-Rodríguez Copyright © 2017 L. Gómez-Valle et al. All rights reserved. Three Different Methods for New Soliton Solutions of the Generalized NLS Equation Wed, 18 Oct 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/5137946/ Three different methods are applied to construct new types of solutions of nonlinear evolution equations. First, the Csch method is used to carry out the solutions; then the Extended Tanh-Coth method and the modified simple equation method are used to obtain the soliton solutions. The effectiveness of these methods is demonstrated by applications to the RKL model, the generalized derivative NLS equation. The solitary wave solutions and trigonometric function solutions are obtained. The obtained solutions are very useful in the nonlinear pulse propagation through optical fibers. Anwar Ja’afar Mohamad Jawad Copyright © 2017 Anwar Ja’afar Mohamad Jawad. All rights reserved. On Singular Solutions to PDEs with Turning Point Involving a Quadratic Nonlinearity Wed, 13 Sep 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/9405298/ We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter . The problem involves an irregular singularity in time, as in a recent work of the author and A. Lastra, but possesses also, as a new feature, a turning point at the origin in . We construct a family of sectorial meromorphic solutions obtained as a small perturbation in of a slow curve of the equation in some time scale. We show that the nonsingular parts of these solutions share common formal power series (that generally diverge) in as Gevrey asymptotic expansion of some order depending on data arising both from the turning point and from the irregular singular point of the main problem. Stéphane Malek Copyright © 2017 Stéphane Malek. All rights reserved. A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem Tue, 12 Sep 2017 09:06:02 +0000 http://www.hindawi.com/journals/aaa/2017/7236103/ Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let be maximal monotone, be bounded and of type and be compact with such that lies in (i.e., there exist and such that for all ). A new topological degree theory is developed for operators of the type . The theory is essential because no degree theory and/or existence result is available to address solvability of operator inclusions involving operators of the type , where is not defined everywhere. Consequently, new existence theorems are provided. The existence theorem due to Asfaw and Kartsatos is improved. The theory is applied to prove existence of weak solution (s) for a nonlinear parabolic problem in appropriate Sobolev spaces. Teffera M. Asfaw Copyright © 2017 Teffera M. Asfaw. All rights reserved. Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms Wed, 02 Aug 2017 06:27:23 +0000 http://www.hindawi.com/journals/aaa/2017/3104512/ We investigate global dynamics of the following systems of difference equations , , , where the parameters , , , , , and are positive numbers and the initial conditions and are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space. V. Hadžiabdić, M. R. S. Kulenović, and E. Pilav Copyright © 2017 V. Hadžiabdić et al. All rights reserved. On Weighted Montgomery Identity for Points and Its Associates on Time Scales Sun, 30 Jul 2017 07:57:07 +0000 http://www.hindawi.com/journals/aaa/2017/5234181/ The purpose of this paper is to establish a weighted Montgomery identity for points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for points. For we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction. Eze R. Nwaeze and Ana M. Tameru Copyright © 2017 Eze R. Nwaeze and Ana M. Tameru. All rights reserved. The Approximation Szász-Chlodowsky Type Operators Involving Gould-Hopper Type Polynomials Wed, 26 Jul 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/4013958/ We introduce the Szász and Chlodowsky operators based on Gould-Hopper polynomials and study the statistical convergence of these operators in a weighted space of functions on a positive semiaxis. Further, a Voronovskaja type result is obtained for the operators containing Gould-Hopper polynomials. Finally, some graphical examples for the convergence of this type of operator are given. Behar Baxhaku and Artan Berisha Copyright © 2017 Behar Baxhaku and Artan Berisha. All rights reserved. Generalized Hölder’s and Minkowski’s Inequalities for Jackson’s -Integral and Some Applications to the Incomplete -Gamma Function Sun, 16 Jul 2017 08:30:14 +0000 http://www.hindawi.com/journals/aaa/2017/9796873/ We establish some generalized Hölder’s and Minkowski’s inequalities for Jackson’s -integral. As applications, we derive some inequalities involving the incomplete -Gamma function. Kwara Nantomah Copyright © 2017 Kwara Nantomah. All rights reserved. A New Class of Contraction in -Metric Spaces and Applications Sun, 11 Jun 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/9718535/ A novel class of --contraction for a pair of mappings is introduced in the setting of -metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation. Preeti Kaushik, Sanjay Kumar, and Kenan Tas Copyright © 2017 Preeti Kaushik et al. All rights reserved. Weak and Strong Solutions for a Strongly Damped Quasilinear Membrane Equation Sun, 11 Jun 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/4529847/ We consider a strongly damped quasilinear membrane equation with Dirichlet boundary condition. The goal is to prove the well-posedness of the equation in weak and strong senses. By setting suitable function spaces and making use of the properties of the quasilinear term in the equation, we have proved the fundamental results on existence, uniqueness, and continuous dependence on data including bilinear term of weak and strong solutions. Jin-soo Hwang Copyright © 2017 Jin-soo Hwang. All rights reserved. Approximation of Durrmeyer Type Operators Depending on Certain Parameters Tue, 30 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/5316150/ Motivated by a number of recent investigations, we consider a new analogue of Bernstein-Durrmeyer operators based on certain variants. We derive some approximation properties of these operators. We also compute local approximation and Voronovskaja type asymptotic formula. We illustrate the convergence of aforementioned operators by making use of the software MATLAB which we stated in the paper. Neha Malik, Serkan Araci, and Man Singh Beniwal Copyright © 2017 Neha Malik et al. All rights reserved. On the Convergence of the Uniform Attractor for the 2D Leray-α Model Wed, 17 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/1681857/ We consider a nonautonomous 2D Leray- model of fluid turbulence. We prove the existence of the uniform attractor . We also study the convergence of as goes to zero. More precisely, we prove that the uniform attractor converges to the uniform attractor of the 2D Navier-Stokes system as tends to zero. Gabriel Deugoué Copyright © 2017 Gabriel Deugoué. All rights reserved. Corrigendum to “Existence of Solutions for a Coupled System of Second and Fourth Order Elliptic Equations” Thu, 11 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/1439729/ Fanglei Wang Copyright © 2017 Fanglei Wang. All rights reserved. On the Boundedness of the Fractional Bergman Operators Wed, 10 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/8363478/ We give a necessary and sufficient condition for the boundedness of the Bergman fractional operators. Benoît F. Sehba Copyright © 2017 Benoît F. Sehba. All rights reserved. Nonnegative Infinite Matrices that Preserve -Convexity of Sequences Tue, 02 May 2017 08:18:23 +0000 http://www.hindawi.com/journals/aaa/2017/9167069/ This paper deals with matrix transformations that preserve the -convexity of sequences. The main result gives the necessary and sufficient conditions for a nonnegative infinite matrix to preserve the -convexity of sequences. Further, we give examples of such matrices for different values of and . Chikkanna R. Selvaraj and Suguna Selvaraj Copyright © 2017 Chikkanna R. Selvaraj and Suguna Selvaraj. All rights reserved. Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales Tue, 18 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/9140138/ We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô’s formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov’s change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale (-time scale). Wenqing Hu Copyright © 2017 Wenqing Hu. All rights reserved. New Conditions for the Exponential Stability of Nonlinear Differential Equations Mon, 10 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/4640835/ We develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coefficients and nonlinear perturbations. Testable conditions for local exponential stability of pseudo-linear differential systems are given. Besides, we establish the robustness of the exponential stability in finite-dimensional spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. We illustrate the application of this test to linear approximations of the differential systems under consideration. Rigoberto Medina Copyright © 2017 Rigoberto Medina. All rights reserved. On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness Tue, 21 Mar 2017 07:02:36 +0000 http://www.hindawi.com/journals/aaa/2017/9323181/ In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities. Nimete Sh. Berisha, Faton M. Berisha, Mikhail K. Potapov, and Marjan Dema Copyright © 2017 Nimete Sh. Berisha et al. All rights reserved. Some Notes about the Continuous-in-Time Financial Model Tue, 21 Mar 2017 06:19:03 +0000 http://www.hindawi.com/journals/aaa/2017/6985820/ In this paper, we investigate the properties of operators in the continuous-in-time model which is designed to be used for the finances of public institutions. These operators are involved in the inverse problem of this model. We discuss this inverse problem in Schwartz space that we prove the uniqueness theorem. Tarik Chakkour Copyright © 2017 Tarik Chakkour. All rights reserved.