International Journal of Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. System of Operator Quasi Equilibrium Problems Thu, 19 Jun 2014 06:43:32 +0000 http://www.hindawi.com/journals/ijanal/2014/848206/ We consider a system of operator quasi equilibrium problems and system of generalized quasi operator equilibrium problems in topological vector spaces. Using a maximal element theorem for a family of set-valued mappings as basic tool, we derive some existence theorems for solutions to these problems with and without involving -condensing mappings. Suhel Ahmad Khan Copyright © 2014 Suhel Ahmad Khan. All rights reserved. On the Spectral Properties of the Weighted Mean Difference Operator over the Sequence Space Mon, 16 Jun 2014 08:56:02 +0000 http://www.hindawi.com/journals/ijanal/2014/786437/ In the present work the generalized weighted mean difference operator has been introduced by combining the generalized weighted mean and difference operator under certain special cases of sequences and . For any two sequences and of either constant or strictly decreasing real numbers satisfying certain conditions the difference operator is defined by with for all . Furthermore, we compute the spectrum and the fine spectrum of the operator over the sequence space . In fact, we determine the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of this operator on the sequence space . P. Baliarsingh and S. Dutta Copyright © 2014 P. Baliarsingh and S. Dutta. All rights reserved. Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications Sun, 15 Jun 2014 05:34:37 +0000 http://www.hindawi.com/journals/ijanal/2014/404186/ We study, for some subsets of , the Banach space of bounded real sequences . For any integer , we introduce a measure over that generalizes the -dimensional Lebesgue measure; consequently, also a theory of integration is defined. The main result of our paper is a change of variables' formula for the integration. Claudio Asci Copyright © 2014 Claudio Asci. All rights reserved. Frames of Eigenfunctions Associated with a Boundary Value Problem Thu, 05 Jun 2014 09:53:36 +0000 http://www.hindawi.com/journals/ijanal/2014/590324/ We introduce and study a redundant system of retro Banach frames consisting of eigenfunctions associated with a given boundary value problem. L. K. Vashisht and Shalu Sharma Copyright © 2014 L. K. Vashisht and Shalu Sharma. All rights reserved. On Nonautonomous Discrete Dynamical Systems Mon, 02 Jun 2014 13:14:48 +0000 http://www.hindawi.com/journals/ijanal/2014/538691/ We define and study expansiveness, shadowing, and topological stability for a nonautonomous discrete dynamical system induced by a sequence of homeomorphisms on a metric space. Dhaval Thakkar and Ruchi Das Copyright © 2014 Dhaval Thakkar and Ruchi Das. All rights reserved. Some Properties of Generalized Gegenbauer Matrix Polynomials Thu, 29 May 2014 09:23:32 +0000 http://www.hindawi.com/journals/ijanal/2014/780649/ Various new generalized forms of the Gegenbauer matrix polynomials are introduced using the integral representation method, which allows us to express them in terms of Hermite matrix polynomials. Certain properties for these new generalized Gegenbauer matrix polynomials such as recurrence relations and expansion in terms of Hermite matrix polynomials are derived. Further, several families of bilinear and bilateral generating matrix relations for these polynomials are established and their applications are presented. Ghazala Yasmin Copyright © 2014 Ghazala Yasmin. All rights reserved. Some New Difference Sequence Spaces of Invariant Means Defined by Ideal and Modulus Function Wed, 28 May 2014 11:29:25 +0000 http://www.hindawi.com/journals/ijanal/2014/631301/ The main objective of this paper is to introduce a new kind of sequence spaces by combining the concepts of modulus function, invariant means, difference sequences, and ideal convergence. We also examine some topological properties of the resulting sequence spaces. Further, we introduce a new concept of -convergence and obtain a condition under which this convergence coincides with above-mentioned sequence spaces. Sudhir Kumar, Vijay Kumar, and S. S. Bhatia Copyright © 2014 Sudhir Kumar et al. All rights reserved. Solvability of a Third-Order Singular Generalized Left Focal Problem in Banach Spaces Mon, 26 May 2014 08:11:58 +0000 http://www.hindawi.com/journals/ijanal/2014/638976/ We consider the existence of positive solution for a third-order singular generalized left focal boundary value problem with full derivatives in Banach spaces. Green’s function and its properties, explicit a priori, estimates will be presented. By means of the theories of the fixed point in cones, we establish some new and general results on the existence of single and multiple positive solutions to the third-order singular generalized left focal boundary value problem. Our results are generalizations and extensions of the results of the focal boundary value problem. An example is included to illustrate the results obtained. Youwei Zhang Copyright © 2014 Youwei Zhang. All rights reserved. Hermite-Hadamard and Simpson Type Inequalities for Differentiable P-GA-Functions Thu, 22 May 2014 08:26:35 +0000 http://www.hindawi.com/journals/ijanal/2014/125439/ The author introduces the concept of the -GA-functions, gives Hermite-Hadamard's inequalities for -GA-functions, and defines a new identity. By using this identity, the author obtains new estimates on generalization of Hadamard and Simpson type inequalities for -GA-functions. Some applications to special means of real numbers are also given. İmdat İşcan Copyright © 2014 İmdat İşcan. All rights reserved. New Relations Involving an Extended Multiparameter Hurwitz-Lerch Zeta Function with Applications Tue, 13 May 2014 07:33:01 +0000 http://www.hindawi.com/journals/ijanal/2014/680850/ We derive several new expansion formulas involving an extended multiparameter Hurwitz-Lerch zeta function introduced and studied recently by Srivastava et al. (2011). These expansions are obtained by using some fractional calculus methods such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. Several (known or new) special cases are also given. H. M. Srivastava, Sébastien Gaboury, and Richard Tremblay Copyright © 2014 H. M. Srivastava et al. All rights reserved. The Hopf Bifurcation Analysis and Optimal Control of a Delayed SIR Epidemic Model Wed, 07 May 2014 11:34:29 +0000 http://www.hindawi.com/journals/ijanal/2014/940819/ We propose a delayed SIR model with saturated incidence rate. The delay is incorporated into the model in order to model the latent period. The basic reproductive number is obtained. Furthermore, using time delay as a bifurcation parameter, it is proven that there exists a critical value of delay for the stability of diseases prevalence. When the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs. The model is extended to assess the impact of some control measures, by reformulating the model as an optimal control problem with vaccination and treatment. The existence of the optimal control is also proved. Finally, some numerical simulations are performed to verify the theoretical analysis. Abdelhadi Abta, Hassan Laarabi, and Hamad Talibi Alaoui Copyright © 2014 Abdelhadi Abta et al. All rights reserved. An Estimate of the Rate of Convergence of the Fourier Series in the Generalized Hölder Metric by Delayed Arithmetic Mean Wed, 07 May 2014 08:27:36 +0000 http://www.hindawi.com/journals/ijanal/2014/171675/ We study the rate of convergence problem of the Fourier series by Delayed Arithmetic Mean in the generalized Hölder metric space which was earlier introduced by Das, Nath, and Ray and obtain a sharper estimate of Jackson's order. L. Nayak, G. Das, and B. K. Ray Copyright © 2014 L. Nayak et al. All rights reserved. Existence and Nonexistence of a Solution for a Nonlinear -Elliptic Problem with Right-Hand Side Measure Sun, 04 May 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijanal/2014/320527/ We discuss the existence and nonexistence of solution of a nonlinear problem -elliptic-, where is a Radon measure with bounded total variation, by considering the Sobolev spaces with variable exponents. This study is done in two cases: (i) is absolutely continuous with respect to -capacity. and (ii) is concentrated on a Borel set of null -capacity. Elhoussine Azroul, Abdelkrim Barbara, and Hicham Redwane Copyright © 2014 Elhoussine Azroul et al. All rights reserved. On Convergence with respect to an Ideal and a Family of Matrices Thu, 24 Apr 2014 10:13:45 +0000 http://www.hindawi.com/journals/ijanal/2014/490904/ P. Das et al. recently introduced and studied the notions of strong -summability with respect to an Orlicz function and -statistical convergence, where is a nonnegative regular matrix and is an ideal on the set of natural numbers. In this paper, we will generalise these notions by replacing with a family of matrices and with a family of Orlicz functions or moduli and study the thus obtained convergence methods. We will also give an application in Banach space theory, presenting a generalisation of Simons' sup-limsup-theorem to the newly introduced convergence methods (for the case that the filter generated by the ideal has a countable base), continuing some of the author's previous work. Jan-David Hardtke Copyright © 2014 Jan-David Hardtke. All rights reserved. On the Logarithmic Regularity Conditions for the Variable Exponent Hardy Type Inequality Wed, 23 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijanal/2014/606012/ We discuss a logarithmic regularity condition in a neighborhood of the origin and infinity on the exponent functions and for the variable exponent Hardy inequality to hold. Aziz Harman and Mustafa Özgür Keleş Copyright © 2014 Aziz Harman and Mustafa Özgür Keleş. All rights reserved. New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals Tue, 22 Apr 2014 12:12:05 +0000 http://www.hindawi.com/journals/ijanal/2014/353924/ The author obtains new estimates on generalization of Hadamard, Ostrowski, and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive real numbers are also given. İmdat İşcan Copyright © 2014 İmdat İşcan. All rights reserved. Initial Coefficient Bounds for a General Class of Biunivalent Functions Wed, 16 Apr 2014 11:53:26 +0000 http://www.hindawi.com/journals/ijanal/2014/867871/ We find estimates on the coefficients and for functions in the function class . The results presented in this paper improve or generalize the recent work of Srutha Keerthi and Raja (2013). Şahsene Altınkaya and Sibel Yalçın Copyright © 2014 Şahsene Altınkaya and Sibel Yalçın. All rights reserved. Unexpected Solutions of the Nehari Problem Thu, 10 Apr 2014 09:40:17 +0000 http://www.hindawi.com/journals/ijanal/2014/467831/ The Nehari characteristic numbers are the minimal values of an integral functional associated with a boundary value problem (BVP) for nonlinear ordinary differential equation. In case of multiple solutions of the BVP, the problem of identifying of minimizers arises. It was observed earlier that for nonoscillatory (positive) solutions of BVP those with asymmetric shape can provide the minimal value to a functional. At the same time, an even solution with regular shape is not a minimizer. We show by constructing the example that the same phenomenon can be observed in the Nehari problem for the fifth characteristic number which is associated with oscillatory solutions of BVP (namely, with those having exactly four zeros in . A. Gritsans and F. Sadyrbaev Copyright © 2014 A. Gritsans and F. Sadyrbaev. All rights reserved. Jensen Functionals on Time Scales for Several Variables Thu, 10 Apr 2014 07:43:15 +0000 http://www.hindawi.com/journals/ijanal/2014/126797/ We define Jensen functionals and concerned generalized means for several variables on time scales. We derive properties of Jensen functionals and apply them to generalized means. In this setting, we obtain generalizations, refinements, and conversions of many remarkable inequalities. Matloob Anwar, Rabia Bibi, Martin Bohner, and Josip Pečarić Copyright © 2014 Matloob Anwar et al. All rights reserved. On the Inequalities for the Generalized Trigonometric Functions Mon, 07 Apr 2014 07:34:14 +0000 http://www.hindawi.com/journals/ijanal/2014/319837/ This paper deals with Huygens-type and Wilker-type inequalities for the generalized trigonometric functions of P. Lindqvist. A major mathematical tool used in this work is a generalized version of the Schwab-Borchardt mean introduced recently by the author of this work. Edward Neuman Copyright © 2014 Edward Neuman. All rights reserved. Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator Sun, 06 Apr 2014 06:29:21 +0000 http://www.hindawi.com/journals/ijanal/2014/793709/ Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed. K. Vijaya, G. Murugusundaramoorthy, and M. Kasthuri Copyright © 2014 K. Vijaya et al. All rights reserved. On a Pointwise Convergence of Quasi-Periodic-Rational Trigonometric Interpolation Thu, 03 Apr 2014 13:37:13 +0000 http://www.hindawi.com/journals/ijanal/2014/249513/ We introduce a procedure for convergence acceleration of the quasi-periodic trigonometric interpolation by application of rational corrections which leads to quasi-periodic-rational trigonometric interpolation. Rational corrections contain unknown parameters whose determination is important for realization of interpolation. We investigate the pointwise convergence of the resultant interpolation for special choice of the unknown parameters and derive the exact constants of the main terms of asymptotic errors. Arnak Poghosyan and Lusine Poghosyan Copyright © 2014 Arnak Poghosyan and Lusine Poghosyan. All rights reserved. Some Properties of -Locally Closed Sets Mon, 31 Mar 2014 06:40:12 +0000 http://www.hindawi.com/journals/ijanal/2014/393618/ A new kind of generalization of (1, 2)*-closed set, namely, (1, 2)*-locally closed set, is introduced and using (1, 2)*-locally closed sets we study the concept of (1, 2)*-LC-continuity in bitopological space. Also we study (1, 2)*-contracontinuity and lastly investigate its relationship with (1, 2)*-LC-continuity. Baby Bhattacharya, Arnab Paul, and Sudip Debnath Copyright © 2014 Baby Bhattacharya et al. All rights reserved. On the -Biharmonic Operator with Critical Sobolev Exponent and Nonlinear Steklov Boundary Condition Wed, 19 Mar 2014 11:35:48 +0000 http://www.hindawi.com/journals/ijanal/2014/498386/ We show that this operator possesses at least one nondecreasing sequence of positive eigenvalues. A direct characterization of the principal eigenvalue (the first one) is given that we apply to study the spectrum of the -biharmonic operator with a critical Sobolev exponent and the nonlinear Steklov boundary conditions using variational arguments and trace critical Sobolev embedding. Abdelouahed El Khalil, My Driss Morchid Alaoui, and Abdelfattah Touzani Copyright © 2014 Abdelouahed El Khalil et al. All rights reserved. On Solutions for a Generalized Differential Equation Arising in Boundary Layer Problem Tue, 18 Mar 2014 08:13:06 +0000 http://www.hindawi.com/journals/ijanal/2014/472698/ We treat the existence and uniqueness of a solution for the generalized Blasius problem which arises in boundary layer theory. The shooting method is used in the proof of our main result. An example is included to illustrate the results. Sergey Smirnov Copyright © 2014 Sergey Smirnov. All rights reserved. Coupled Fixed Point Theorems for ()-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications Tue, 18 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijanal/2014/586096/ The object of this paper is to establish the existence and uniqueness of coupled fixed points under a (, )-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012) and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006), and Luong and Thuan (2011). The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations. Manish Jain, Neetu Gupta, and Sanjay Kumar Copyright © 2014 Manish Jain et al. All rights reserved. Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem Sun, 16 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijanal/2014/280709/ We study the existence of solutions of a nonlinear Volterra integral equation in the space . With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results. Mahmoud Bousselsal and Sidi Hamidou Jah Copyright © 2014 Mahmoud Bousselsal and Sidi Hamidou Jah. All rights reserved. Fekete-Szegö Type Coefficient Inequalities for Certain Subclass of Analytic Functions and Their Applications Involving the Owa-Srivastava Fractional Operator Thu, 13 Mar 2014 16:15:18 +0000 http://www.hindawi.com/journals/ijanal/2014/490359/ A new subclass of analytic functions is introduced. For this class, firstly the Fekete-Szegö type coefficient inequalities are derived. Various known or new special cases of our results are also pointed out. Secondly some applications of our main results involving the Owa-Srivastava fractional operator are considered. Thus, as one of these applications of our result, we obtain the Fekete-Szegö type inequality for a class of normalized analytic functions, which is defined here by means of the Hadamard product (or convolution) and the Owa-Srivastava fractional operator. Serap Bulut Copyright © 2014 Serap Bulut. All rights reserved. Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces Tue, 11 Mar 2014 09:27:55 +0000 http://www.hindawi.com/journals/ijanal/2014/258389/ Aseev launched a new branch of functional analysis by introducing the theory of quasilinear spaces in the framework of the topics of norm, bounded quasilinear operators and functionals (Aseev (1986)). Furthermore, some quasilinear counterparts of classical nonlinear analysis that lead to such result as Frechet derivative and its applications were examined deal with. This pioneering work causes a lot of results in such applications such as (Rojas-Medar et al. (2005), Talo and Başar (2010), and Nikol'skiĭ (1993)). His work has motivated us to introduce the concept of quasilinear inner product spaces. Thanks to this new notion, we obtain some new theorems and definitions which are quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. We claim that some new results related to this concept provide an important contribution to the improvement of quasilinear functional analysis. Hacer Bozkurt, Sümeyye Çakan, and Yılmaz Yılmaz Copyright © 2014 Hacer Bozkurt et al. All rights reserved. Second Order Ideal-Ward Continuity Wed, 05 Mar 2014 13:28:12 +0000 http://www.hindawi.com/journals/ijanal/2014/480918/ The main aim of the paper is to introduce a concept of second order ideal-ward continuity in the sense that a function is second order ideal-ward continuous if whenever and a concept of second order ideal-ward compactness in the sense that a subset of is second order ideal-ward compact if any sequence of points in has a subsequence of the sequence x such that where . We investigate the impact of changing the definition of convergence of sequences on the structure of ideal-ward continuity in the sense of second order ideal-ward continuity and compactness of sets in the sense of second order ideal-ward compactness and prove related theorems. Bipan Hazarika Copyright © 2014 Bipan Hazarika. All rights reserved.