Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . 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. On a Degenerate Evolution System Associated with the Bean Critical-State for Type II Superconductors Thu, 31 Dec 2015 06:34:38 +0000 http://www.hindawi.com/journals/aaa/2015/875190/ We study a degenerate evolution system containing the -curl system in a bounded domain with initial and boundary conditions for the magnetic field under the influence of a system force . This is concerned with an approximation of Bean’s critical-state model for type II superconductors. We will show the existence, uniqueness, and regularity of solutions. Moreover we will get the properties of the limit solution as . Junichi Aramaki Copyright © 2015 Junichi Aramaki. All rights reserved. On -Bleimann, Butzer, and Hahn-Type Operators Tue, 29 Dec 2015 13:19:59 +0000 http://www.hindawi.com/journals/aaa/2015/480925/ Sequence of -Bleimann, Butzer, and Hahn operators which is based on a continuously differentiable function on , with , , has been considered. Uniform approximation by such a sequence has been studied and degree of approximation by the operators has been obtained. Moreover, shape preserving properties of the sequence of operators have been investigated. Dilek Söylemez Copyright © 2015 Dilek Söylemez. All rights reserved. Existence and Uniqueness Results for Fractional Differential Equations with Riemann-Liouville Fractional Integral Boundary Conditions Tue, 29 Dec 2015 13:00:48 +0000 http://www.hindawi.com/journals/aaa/2015/290674/ We prove the existence and uniqueness of solution for fractional differential equations with Riemann-Liouville fractional integral boundary conditions. The first existence and uniqueness result is based on Banach’s contraction principle. Moreover, other existence results are also obtained by using the Krasnoselskii fixed point theorem. An example is given to illustrate the main results. Mohamed I. Abbas Copyright © 2015 Mohamed I. Abbas. All rights reserved. Generalized Variability Orderings among Nonnegative Fuzzy Random Variables Tue, 29 Dec 2015 08:45:25 +0000 http://www.hindawi.com/journals/aaa/2015/757943/ The variability ordering for more and less variables of fuzzy random variables in terms of its distribution function is defined. A property of new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) is derived as an application to the variability ordering of fuzzy random variables. The concept of generalized variability orderings of nonnegative fuzzy random variables representing lifetime of components is introduced. The domination is a generalized variability ordering. We proposed an integral inequality to the case of fuzzy random variables using ordering. The results included equivalent conditions which justify the generalized variability orderings. S. Ramasubramanian and P. Mahendran Copyright © 2015 S. Ramasubramanian and P. Mahendran. All rights reserved. A Semilinear Wave Equation with a Boundary Condition of Many-Point Type: Global Existence and Stability of Weak Solutions Sun, 27 Dec 2015 07:29:03 +0000 http://www.hindawi.com/journals/aaa/2015/531872/ This paper is devoted to the study of a wave equation with a boundary condition of many-point type. The existence of weak solutions is proved by using the Galerkin method. Also, the uniqueness and the stability of solutions are established. Giai Giang Vo Copyright © 2015 Giai Giang Vo. All rights reserved. Positive Solutions for Nonlinear -Fractional Difference Eigenvalue Problem with Nonlocal Conditions Mon, 21 Dec 2015 06:25:15 +0000 http://www.hindawi.com/journals/aaa/2015/759378/ The problem of positive solutions for nonlinear -fractional difference eigenvalue problem with nonlocal boundary conditions is investigated. Based on the fixed point index theory in cones, sufficient existence of positive solutions conditions is derived for the problem. Wafa Shammakh and Maryam Al-Yami Copyright © 2015 Wafa Shammakh and Maryam Al-Yami. All rights reserved. Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem Tue, 15 Dec 2015 12:40:13 +0000 http://www.hindawi.com/journals/aaa/2015/659072/ The existence and uniqueness of a mild solution to nonlinear fuzzy differential equation constrained by initial value were proven. Initial value constraint was then replaced by delay function constraint and the existence of a solution to this type of problem was also proven. Furthermore, the existence of a solution to optimal control problem of the latter type of equation was proven. Wichai Witayakiattilerd Copyright © 2015 Wichai Witayakiattilerd. All rights reserved.