Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Existence of General Competitive Equilibria: A Variational Approach Mon, 20 Jun 2016 14:28:46 +0000 http://www.hindawi.com/journals/aaa/2016/4969253/ We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities. G. Anello and F. Rania Copyright © 2016 G. Anello and F. Rania. All rights reserved. Twist Periodic Solutions in the Relativistic Driven Harmonic Oscillator Mon, 13 Jun 2016 12:23:30 +0000 http://www.hindawi.com/journals/aaa/2016/6084082/ We study the one-dimensional forced harmonic oscillator with relativistic effects. Under some conditions of the parameters, the existence of a unique stable periodic solution is proved which is of twist type. The results depend on a Twist Theorem for nonlinear Hill’s equations which is established and proved here. Daniel Núñez and Andrés Rivera Copyright © 2016 Daniel Núñez and Andrés Rivera. All rights reserved. Existence of Solutions for a Robin Problem Involving the -Laplace Operator Mon, 13 Jun 2016 07:45:05 +0000 http://www.hindawi.com/journals/aaa/2016/2349172/ In this article we study the nonlinear Robin boundary-value problem , on . Using the variational method, under appropriate assumptions on , we obtain results on existence and multiplicity of solutions. Mostafa Allaoui Copyright © 2016 Mostafa Allaoui. All rights reserved. A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem Thu, 02 Jun 2016 11:28:21 +0000 http://www.hindawi.com/journals/aaa/2016/1304954/ We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods. Mio Horai, Hideo Kobayashi, and Takashi G. Nitta Copyright © 2016 Mio Horai et al. All rights reserved. Consistent Approximations of the Zeno Behaviour in Affine-Type Switched Dynamic Systems Wed, 01 Jun 2016 08:02:36 +0000 http://www.hindawi.com/journals/aaa/2016/2091526/ This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes. Vadim Azhmyakov Copyright © 2016 Vadim Azhmyakov. All rights reserved. On Certain Properties for Two Classes of Generalized Convex Functions Thu, 26 May 2016 13:00:40 +0000 http://www.hindawi.com/journals/aaa/2016/4652038/ Two classes of generalized convex functions in the sense of Beckenbach are considered. For both classes, we show that the existence of support curves implies their generalized convexity and obtain an extremum property of these functions. Furthermore, we establish Hadamard’s inequality for them. Mohamed S. S. Ali Copyright © 2016 Mohamed S. S. Ali. All rights reserved. On Estimates of Deviation of Functions from Matrix Operators of Their Fourier Series by Some Expressions with -Differences of the Entries Sun, 22 May 2016 08:45:37 +0000 http://www.hindawi.com/journals/aaa/2016/9712878/ We generalize the results of Krasniqi 2012 and Wei and Yu 2012 to the case of -differences. Włodzimierz Łenski and Bogdan Szal Copyright © 2016 Włodzimierz Łenski and Bogdan Szal. All rights reserved. Certain Subclasses of Bistarlike and Biconvex Functions Based on Quasi-Subordination Thu, 28 Apr 2016 11:55:17 +0000 http://www.hindawi.com/journals/aaa/2016/3102960/ We introduce the unified biunivalent function class defined based on quasi-subordination and obtained the coefficient estimates for Taylor-Maclaurin coefficients and . Several related classes of functions are also considered and connections to earlier known and new results are established. Nanjundan Magesh, Vitalrao Kupparao Balaji, and Jagadesan Yamini Copyright © 2016 Nanjundan Magesh et al. All rights reserved. -Trigonometric and -Hyperbolic Functions in Complex Domain Wed, 27 Apr 2016 09:59:19 +0000 http://www.hindawi.com/journals/aaa/2016/3249439/ We study extension of -trigonometric functions and and of -hyperbolic functions and to complex domain. Our aim is to answer the question under what conditions on these functions satisfy well-known relations for usual trigonometric and hyperbolic functions, such as, for example, . In particular, we prove in the paper that for the -trigonometric and -hyperbolic functions satisfy very analogous relations as their classical counterparts. Our methods are based on the theory of differential equations in the complex domain using the Maclaurin series for -trigonometric and -hyperbolic functions. Petr Girg and Lukáš Kotrla Copyright © 2016 Petr Girg and Lukáš Kotrla. All rights reserved. A Computational Study of the Boundary Value Methods and the Block Unification Methods for Mon, 11 Apr 2016 13:05:19 +0000 http://www.hindawi.com/journals/aaa/2016/8465103/ We derive a new class of linear multistep methods (LMMs) via the interpolation and collocation technique. We discuss the use of these methods as boundary value methods and block unification methods for the numerical approximation of the general second-order initial and boundary value problems. The convergence of these families of methods is also established. Several test problems are given to show a computational comparison of these methods in terms of accuracy and the computational efficiency. T. A. Biala Copyright © 2016 T. A. Biala. All rights reserved. Random First-Order Linear Discrete Models and Their Probabilistic Solution: A Comprehensive Study Mon, 11 Apr 2016 11:32:49 +0000 http://www.hindawi.com/journals/aaa/2016/6372108/ This paper presents a complete stochastic solution represented by the first probability density function for random first-order linear difference equations. The study is based on Random Variable Transformation method. The obtained results are given in terms of the probability density functions of the data, namely, initial condition, forcing term, and diffusion coefficient. To conduct the study, all possible cases regarding statistical dependence of the random input parameters are considered. A complete collection of illustrative examples covering all the possible scenarios is provided. M.-C. Casabán, J.-C. Cortés, J.-V. Romero, and M.-D. Roselló Copyright © 2016 M.-C. Casabán et al. All rights reserved. New Conditions for the Exponential Stability of Pseudolinear Difference Equations in Banach Spaces Thu, 07 Apr 2016 06:06:10 +0000 http://www.hindawi.com/journals/aaa/2016/5098086/ We study the local exponential stability of evolution difference systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in infinite-dimensional Banach spaces, in the sense that the exponential stability for a given pseudolinear equation persists under sufficiently small perturbations. The main methodology is based on a combined use of new norm estimates for operator-valued functions with the “freezing” method. Rigoberto Medina Copyright © 2016 Rigoberto Medina. All rights reserved. The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators Sun, 27 Mar 2016 11:44:04 +0000 http://www.hindawi.com/journals/aaa/2016/2371857/ We investigate the convergence analysis of the following general inexact algorithm for approximating a zero of the sum of a cocoercive operator and maximal monotone operators with : , for for given in a real Hilbert space , where , , and are sequences in with for all , denotes the error sequence, and is a contraction. The algorithm is known to converge under the following assumptions on and : (i) is bounded below away from 0 and above away from 1 and (ii) is summable in norm. In this paper, we show that these conditions can further be relaxed to, respectively, the following: (i) is bounded below away from 0 and above away from 3/2 and (ii) is square summable in norm; and we still obtain strong convergence results. Oganeditse Aaron Boikanyo Copyright © 2016 Oganeditse Aaron Boikanyo. All rights reserved. Approximation of a Common Element of the Fixed Point Sets of Multivalued Strictly Pseudocontractive-Type Mappings and the Set of Solutions of an Equilibrium Problem in Hilbert Spaces Wed, 16 Mar 2016 13:54:52 +0000 http://www.hindawi.com/journals/aaa/2016/3094838/ The strong convergence of a hybrid algorithm to a common element of the fixed point sets of multivalued strictly pseudocontractive-type mappings and the set of solutions of an equilibrium problem in Hilbert spaces is obtained using a strict fixed point set condition. The obtained results improve, complement, and extend the results on multivalued and single-valued mappings in the contemporary literature. F. O. Isiogugu Copyright © 2016 F. O. Isiogugu. All rights reserved. Tridiagonal Operators and Zeros of Polynomials in Two Variables Wed, 16 Mar 2016 08:27:28 +0000 http://www.hindawi.com/journals/aaa/2016/6301413/ The aim of this paper is to connect the zeros of polynomials in two variables with the eigenvalues of a self-adjoint operator. This is done by use of a functional-analytic method. The polynomials in two variables are assumed to satisfy a five-term recurrence relation, similar to the three-term recurrence relation that the classical orthogonal polynomials satisfy. Chrysi G. Kokologiannaki, Eugenia N. Petropoulou, and Dimitris Rizos Copyright © 2016 Chrysi G. Kokologiannaki et al. All rights reserved. Corrigendum to “A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion” Sun, 13 Mar 2016 12:32:29 +0000 http://www.hindawi.com/journals/aaa/2016/8037807/ José Antonio López Ortí, Francisco José Marco Castillo, and María José Martínez Usó Copyright © 2016 José Antonio López Ortí et al. All rights reserved. Existence of Infinitely Many Periodic Solutions for Perturbed Semilinear Fourth-Order Impulsive Differential Inclusions Sun, 06 Mar 2016 10:37:37 +0000 http://www.hindawi.com/journals/aaa/2016/5784273/ This paper discusses the existence of infinitely many periodic solutions for a semilinear fourth-order impulsive differential inclusion with a perturbed nonlinearity and two parameters. The approach is based on a critical point theorem for nonsmooth functionals. Massimiliano Ferrara, Giuseppe Caristi, and Amjad Salari Copyright © 2016 Massimiliano Ferrara et al. All rights reserved. On the Property Thu, 03 Mar 2016 06:55:45 +0000 http://www.hindawi.com/journals/aaa/2016/1256906/ We construct a continuous function such that possesses -property, but does not have approximate derivative on a set of full Lebesgue measure. This shows that Banach’s Theorem concerning differentiability of continuous functions with Lusin’s property does not hold for -property. Some relevant properties are presented. Stanisław Kowalczyk and Małgorzata Turowska Copyright © 2016 Stanisław Kowalczyk and Małgorzata Turowska. All rights reserved. An Application of Potential Estimates to A Priori Bounds for Elliptic Equations Wed, 24 Feb 2016 14:21:52 +0000 http://www.hindawi.com/journals/aaa/2016/6463030/ A potential estimate type approach is used in order to obtain some a priori bounds for the solutions of certain classes of Dirichlet problems associated with nondivergence structure elliptic equations. Farman Mamedov, Sara Monsurrò, and Maria Transirico Copyright © 2016 Farman Mamedov et al. All rights reserved. Convex Sweeping Processes with Noncompact Perturbations and with Delay in Banach Spaces Tue, 23 Feb 2016 13:56:19 +0000 http://www.hindawi.com/journals/aaa/2016/3853205/ We prove two results concerning the existence of solutions for functional differential inclusions that are governed by sweeping processes, with noncompact valued perturbations in Banach spaces. Indeed, we have two goals. The first is to give a technique that allows considering sweeping processes with noncompact valued perturbations and associated with a multivalued function depending on time. The second is to give a technique to overcome the arising problem from the nonlinearity of the normalized mappings, when we deal with sweeping processes with noncompact valued perturbations and associated with a multivalued function depending on time and state. A. G. Ibrahim and F. Aladsani Copyright © 2016 A. G. Ibrahim and F. Aladsani. All rights reserved. Density by Moduli and Lacunary Statistical Convergence Mon, 15 Feb 2016 12:02:30 +0000 http://www.hindawi.com/journals/aaa/2016/9365037/ We have introduced and studied a new concept of -lacunary statistical convergence, where is an unbounded modulus. It is shown that, under certain conditions on a modulus , the concepts of lacunary strong convergence with respect to a modulus and -lacunary statistical convergence are equivalent on bounded sequences. We further characterize those for which , where and denote the sets of all -lacunary statistically convergent sequences and -statistically convergent sequences, respectively. A general description of inclusion between two arbitrary lacunary methods of -statistical convergence is given. Finally, we give an -analog of the Cauchy criterion for convergence and a Tauberian theorem for -convergence is also proved. Vinod K. Bhardwaj and Shweta Dhawan Copyright © 2016 Vinod K. Bhardwaj and Shweta Dhawan. All rights reserved. Density by Moduli and Statistical Boundedness Wed, 10 Feb 2016 09:01:33 +0000 http://www.hindawi.com/journals/aaa/2016/2143018/ We have generalized the notion of statistical boundedness by introducing the concept of -statistical boundedness for scalar sequences where is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are -statistically bounded for every unbounded modulus . A decomposition theorem for -statistical convergence for vector valued sequences and a structure theorem for -statistical boundedness have also been established. Vinod K. Bhardwaj, Shweta Dhawan, and Sandeep Gupta Copyright © 2016 Vinod K. Bhardwaj et al. All rights reserved. Unbounded Solutions for Functional Problems on the Half-Line Sun, 07 Feb 2016 14:01:32 +0000 http://www.hindawi.com/journals/aaa/2016/8987374/ This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green’s functions, and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results. Hugo Carrasco and Feliz Minhós Copyright © 2016 Hugo Carrasco and Feliz Minhós. All rights reserved. Second Hankel Determinants for the Class of Typically Real Functions Wed, 03 Feb 2016 09:18:26 +0000 http://www.hindawi.com/journals/aaa/2016/3792367/ We discuss the Hankel determinants for typically real functions, that is, analytic functions which satisfy the condition in the unit disk Δ. Main results are concerned with and . The sharp upper and lower bounds are given. In general case, for , the results are not sharp. Moreover, we present some remarks connected with typically real odd functions. Paweł Zaprawa Copyright © 2016 Paweł Zaprawa. All rights reserved. Timelike Tangent Developable Surfaces and Bonnet Surfaces Mon, 01 Feb 2016 06:56:19 +0000 http://www.hindawi.com/journals/aaa/2016/6837543/ A criterion was given for a timelike surface to be a Bonnet surface in 3-dimensional Minkowski space by Chen and Li, 1999. In this study, we obtain a necessary and sufficient condition for a timelike tangent developable surface to be a timelike Bonnet surface by the aid of this criterion. This is examined under the condition of the curvature and torsion of the base curve of the timelike developable surface being nonconstant. Moreover, we investigate the nontrivial isometry preserving the mean curvature for a timelike flat helicoidal surface by considering the curvature and torsion of the base curve of the timelike developable surface as being constant. Soley Ersoy and Kemal Eren Copyright © 2016 Soley Ersoy and Kemal Eren. All rights reserved. Behavior of the Solutions for Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on Periodic Time Scales in Shifts Wed, 27 Jan 2016 07:57:32 +0000 http://www.hindawi.com/journals/aaa/2016/1463043/ We consider two-dimensional predator-prey system with Beddington-DeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system has -periodic solution. Neslihan Nesliye Pelen, Ayşe Feza Güvenilir, and Billur Kaymakçalan Copyright © 2016 Neslihan Nesliye Pelen et al. All rights reserved. Best Proximity Point Theorem in Quasi-Pseudometric Spaces Sun, 24 Jan 2016 07:22:04 +0000 http://www.hindawi.com/journals/aaa/2016/9784592/ In quasi-pseudometric spaces (not necessarily sequentially complete), we continue the research on the quasi-generalized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with respect to generalized pseudodistances. Next, inspired by Abkar and Gabeleh we proved new best proximity point theorem in a quasi-pseudometric space. A best proximity point theorem furnishes sufficient conditions that ascertain the existence of an optimal solution to the problem of globally minimizing the error , and hence the existence of a consummate approximate solution to the equation . Robert Plebaniak Copyright © 2016 Robert Plebaniak. All rights reserved. Exact Solutions of Travelling Wave Model via Dynamical System Method Wed, 20 Jan 2016 07:05:38 +0000 http://www.hindawi.com/journals/aaa/2016/9290734/ By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrödinger-Boussinesq equations are studied. Based on this method, the bounded exact travelling wave solutions are obtained which contain solitary wave solutions and periodic travelling wave solutions. The solitary wave solutions and periodic travelling wave solutions are expressed by the hyperbolic functions and the Jacobian elliptic functions, respectively. The results show that the presented findings improve the related previous conclusions. Furthermore, the numerical simulations of the solitary wave solutions and the periodic travelling wave solutions are given to show the correctness of our results. Heng Wang, Longwei Chen, and Hongjiang Liu Copyright © 2016 Heng Wang et al. All rights reserved. Local Hypoellipticity by Lyapunov Function Sun, 17 Jan 2016 13:57:47 +0000 http://www.hindawi.com/journals/aaa/2016/7210540/ We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: , , where is a self-adjoint linear operator, positive with , in a Hilbert space , and is a series of nonnegative powers of with coefficients in , being an open set of , for any , different from what happens in the work of Hounie (1979) who studies the problem only in the case . We provide sufficient condition to get the local hypoellipticity for that complex in the elliptic region, using a Lyapunov function and the dynamics properties of solutions of the Cauchy problem ′, , being the first coefficient of . Besides, to get over the problem out of the elliptic region, that is, in the points ∗  such that ∗ = 0, we will use the techniques developed by Bergamasco et al. (1993) for the particular operator . E. R. Aragão-Costa Copyright © 2016 E. R. Aragão-Costa. All rights reserved. A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform Wed, 06 Jan 2016 11:20:21 +0000 http://www.hindawi.com/journals/aaa/2016/5874930/ We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied. Mawardi Bahri and Ryuichi Ashino Copyright © 2016 Mawardi Bahri and Ryuichi Ashino. All rights reserved.