Abstract and Applied Analysis
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© 2016 , Hindawi Publishing Corporation . 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 pseudoLaplacian. In this way generalized versions for some results which use Ekeland variational principle, critical points for nondifferentiable functionals, and GhoussoubMaurey 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 firstorder, twopoint 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 ArzelaAscoli 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 wellknown 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 meaninequalities 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 NonNewtonian (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 nonNewtonian (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 skinfriction and the heat fluxes are obtained and discussed numerically.
Gamal M. AbdelRahman Rashed and Faiza M. N. Elfayez
Copyright © 2016 Gamal M. AbdelRahman Rashed and Faiza M. N. Elfayez. 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 onedimensional 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 boundaryvalue 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 AffineType 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 Zenotype 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 QuasiSubordination
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 quasisubordination and obtained the coefficient estimates for TaylorMaclaurin 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 wellknown 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 secondorder 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 FirstOrder 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 firstorder 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 infinitedimensional 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 operatorvalued functions with the “freezing” method.
Rigoberto Medina
Copyright © 2016 Rigoberto Medina. All rights reserved.

The Viscosity Approximation ForwardBackward 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 PseudocontractiveType 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 pseudocontractivetype 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 singlevalued 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 selfadjoint operator. This is done by use of a functionalanalytic method. The polynomials in two variables are assumed to satisfy a fiveterm recurrence relation, similar to the threeterm 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 FourthOrder 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 fourthorder 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 HalfLine
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 secondorder differential equation on the halfline 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 EmdenFowler 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 3dimensional 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.