Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Certain Properties of Some Families of Generalized Starlike Functions with respect to -Calculus Sun, 25 Sep 2016 09:46:43 +0000 http://www.hindawi.com/journals/aaa/2016/6180140/ By making use of the concept of -calculus, various types of generalized starlike functions of order were introduced and studied from different viewpoints. In this paper, we investigate the relation between various former types of -starlike functions of order . We also introduce and study a new subclass of -starlike functions of order . Moreover, we give some properties of those -starlike functions with negative coefficient including the radius of univalency and starlikeness. Some illustrative examples are provided to verify the theoretical results in case of negative coefficient functions class. Ben Wongsaijai and Nattakorn Sukantamala Copyright © 2016 Ben Wongsaijai and Nattakorn Sukantamala. All rights reserved. Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness Sun, 18 Sep 2016 10:55:15 +0000 http://www.hindawi.com/journals/aaa/2016/4567092/ We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases and Rodrigo Ponce Copyright © 2016 Rodrigo Ponce. All rights reserved. Generalized Jensen-Mercer Inequality for Functions with Nondecreasing Increments Sun, 18 Sep 2016 08:49:09 +0000 http://www.hindawi.com/journals/aaa/2016/5231476/ In the year 2003, McD Mercer established an interesting variation of Jensen’s inequality and later in 2009 Mercer’s result was generalized to higher dimensions by M. Niezgoda. Recently, Asif et al. has stated an integral version of Niezgoda’s result for convex functions. We further generalize Niezgoda’s integral result for functions with nondecreasing increments and give some refinements with applications. In the way, we generalize an important result, Jensen-Boas inequality, using functions with nondecreasing increments. These results would constitute a valuable addition to Jensen-type inequalities in the literature. Asif R. Khan and Sumayyah Saadi Copyright © 2016 Asif R. Khan and Sumayyah Saadi. All rights reserved. Existence and Uniqueness Results for a Smooth Model of Periodic Infectious Diseases Wed, 14 Sep 2016 11:59:08 +0000 http://www.hindawi.com/journals/aaa/2016/1708527/ We prove the existence of a curve (with respect to the scalar delay) of periodic positive solutions for a smooth model of Cooke-Kaplan’s integral equation by using the implicit function theorem under suitable conditions. We also show a situation in which any bounded solution with a sufficiently small delay is isolated, clearing an asymptotic stability result of Cooke and Kaplan. Guy Degla Copyright © 2016 Guy Degla. All rights reserved. Optimality Conditions for Nondifferentiable Multiobjective Semi-Infinite Programming Problems Wed, 07 Sep 2016 09:43:37 +0000 http://www.hindawi.com/journals/aaa/2016/5367190/ We have considered a multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints. First we studied a Fritz-John type necessary condition. Then, we introduced two constraint qualifications and derive the weak and strong Karush-Kuhn-Tucker (KKT in brief) types necessary conditions for an efficient solution of the considered problem. Finally an extension of a Caristi-Ferrara-Stefanescu result for the ()-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in terms of Clark subdifferential. D. Barilla, G. Caristi, and A. Puglisi Copyright © 2016 D. Barilla et al. All rights reserved. Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions Thu, 01 Sep 2016 11:49:37 +0000 http://www.hindawi.com/journals/aaa/2016/5283263/ We study the existence of solutions for nonlinear boundary value problems , where denotes the boundary conditions on a compact interval , is a homeomorphism such that , and is a continuous function. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree is used. Dionicio Pastor Dallos Santos Copyright © 2016 Dionicio Pastor Dallos Santos. All rights reserved. On the Existence of Infinitely Many Solutions for Nonlocal Systems with Critical Exponents Wed, 31 Aug 2016 08:13:37 +0000 http://www.hindawi.com/journals/aaa/2016/7197542/ We study a class of semilinear nonlocal elliptic systems posed on settings without compact Sobolev embedding. By employing critical point theory and concentration estimates, we prove the existence of infinitely many solutions for values of the dimension , where provided M. Khiddi and R. Echarghaoui Copyright © 2016 M. Khiddi and R. Echarghaoui. All rights reserved. Variational Approaches to Characterize Weak Solutions for Some Problems of Mathematical Physics Equations Thu, 25 Aug 2016 16:54:58 +0000 http://www.hindawi.com/journals/aaa/2016/2071926/ This paper is aimed at providing three versions to solve and characterize weak solutions for Dirichlet problems involving the -Laplacian and the -pseudo-Laplacian. In this way generalized versions for some results which use Ekeland variational principle, critical points for nondifferentiable functionals, and Ghoussoub-Maurey linear principle have been proposed. Three sequences of generalized statements have been developed starting from the most abstract assertions until their applications in characterizing weak solutions for some mathematical physics problems involving the abovementioned operators. Irina Meghea Copyright © 2016 Irina Meghea. All rights reserved. Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions Wed, 24 Aug 2016 18:04:37 +0000 http://www.hindawi.com/journals/aaa/2016/3910972/ We investigate two types of first-order, two-point boundary value problems (BVPs). Firstly, we study BVPs that involve nonlinear difference equations (the “discrete” BVP); and secondly, we study BVPs involving nonlinear ordinary differential equations (the “continuous” BVP). We formulate some sufficient conditions under which the discrete BVP will admit solutions. For this, our choice of methods involves a monotone iterative technique and the method of successive approximations (a.k.a. Picard iterations) in the absence of Lipschitz conditions. Our existence results for the discrete BVP are of a constructive nature and are of independent interest in their own right. We then turn our attention to applying our existence results for the discrete BVP to the continuous BVP. We form new existence results for solutions to the continuous BVP with our methods involving linear interpolation of the data from the discrete BVP, combined with a priori bounds and the convergence Arzela-Ascoli theorem. Thus, our use of discrete BVPs to yield results for the continuous BVP may be considered as a discrete approach to continuous BVPs. Douglas R. Anderson and Christopher C. Tisdell Copyright © 2016 Douglas R. Anderson and Christopher C. Tisdell. All rights reserved. Maximality Theorems on the Sum of Two Maximal Monotone Operators and Application to Variational Inequality Problems Thu, 11 Aug 2016 12:48:53 +0000 http://www.hindawi.com/journals/aaa/2016/7826475/ Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let and be maximal monotone operators. The maximality of the sum of two maximal monotone operators has been an open problem for many years. In this paper, new maximality theorems are proved for under weaker sufficient conditions. These theorems improved the well-known maximality results of Rockafellar who used condition and Browder and Hess who used the quasiboundedness of and condition . In particular, the maximality of is proved provided that , where is a proper, convex, and lower semicontinuous function. Consequently, an existence theorem is proved addressing solvability of evolution type variational inequality problem for pseudomonotone perturbation of maximal monotone operator. Teffera M. Asfaw Copyright © 2016 Teffera M. Asfaw. All rights reserved. On Some Inequalities Involving Three or More Means Mon, 08 Aug 2016 11:39:58 +0000 http://www.hindawi.com/journals/aaa/2016/1249604/ We investigate some results about mean-inequalities involving a large number of bivariate means. As application, we derive a lot of inequalities between four or more means among the standard means known in the literature. Mustapha Raïssouli and Mohamed Chergui Copyright © 2016 Mustapha Raïssouli and Mohamed Chergui. All rights reserved. Studying Radiation and Reaction Effects on Unsteady MHD Non-Newtonian (Walter’s B) Fluid in Porous Medium Tue, 26 Jul 2016 13:43:39 +0000 http://www.hindawi.com/journals/aaa/2016/9262518/ This paper describes the studied effects of thermal radiation and chemical reaction on unsteady MHD non-Newtonian (obeying Walter’s B model) fluid in porous medium. The resulting problems are solved numerically. Graphical results for various interesting parameters are presented. Also the effects of the different parameters on the skin-friction and the heat fluxes are obtained and discussed numerically. Gamal M. Abdel-Rahman Rashed and Faiza M. N. El-fayez Copyright © 2016 Gamal M. Abdel-Rahman Rashed and Faiza M. N. El-fayez. 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.