International Journal of Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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. Growth of Logarithmic Derivatives and Their Applications in Complex Differential Equations Tue, 04 Mar 2014 15:36:29 +0000 http://www.hindawi.com/journals/ijanal/2014/342974/ We continue the study of the behavior of the growth of logarithmic derivatives. In fact, we prove some relations between the value distribution of solutions of linear differential equations and growth of their logarithmic derivatives. We also give an estimate of the growth of the quotient of two differential polynomials generated by solutions of the equation where and are entire functions. Zinelâabidine Latreuch and Benharrat Belaïdi Copyright © 2014 Zinelâabidine Latreuch and Benharrat Belaïdi. All rights reserved. Weighted Fractional Differentiation Composition Operators from Mixed-Norm Spaces to Weighted-Type Spaces Thu, 27 Feb 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijanal/2014/301709/ Let be an open unit disc in the complex plane and let as well as be analytic maps. For an analytic function on the weighted fractional differentiation composition operator is defined as , where , , and . In this paper, we obtain a characterization of boundedness and compactness of weighted fractional differentiation composition operator from mixed-norm space to weighted-type space . D. Borgohain and S. Naik Copyright © 2014 D. Borgohain and S. Naik. All rights reserved. On the Harmonic Problem with Nonlinear Boundary Integral Conditions Sun, 23 Feb 2014 12:57:28 +0000 http://www.hindawi.com/journals/ijanal/2014/976520/ In the present work, we deal with the harmonic problems in a bounded domain of with the nonlinear boundary integral conditions. After applying the Boundary integral method, a nonlinear boundary integral equation is obtained; the existence and uniqueness of the solution will be a consequence of applying theory of monotone operators. Saker Hacene Copyright © 2014 Saker Hacene. All rights reserved. Logarithmically Improved Regularity Criterion for the 3D Micropolar Fluid Equations Thu, 13 Feb 2014 13:56:40 +0000 http://www.hindawi.com/journals/ijanal/2014/386269/ We study the regularity of weak solutions to the incompressible micropolar fluid equations. We obtain an improved regularity criterion in terms of vorticity of velocity in Besov space. It is proved that if the vorticity field satisfies then the strong solution can be smoothly extended after time . Hui Zhang Copyright © 2014 Hui Zhang. All rights reserved. A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations Wed, 12 Feb 2014 12:45:31 +0000 http://www.hindawi.com/journals/ijanal/2014/685796/ Based on iterative method proposed by Basto et al. (2006), we present a new derivative-free iterative method for solving nonlinear equations. The aim of this paper is to develop a new method to find the approximation of the root α of the nonlinear equation . This method has the efficiency index which equals . The benefit of this method is that this method does not need to calculate any derivative. Several examples illustrate that the efficiency of the new method is better than that of previous methods. Tahereh Eftekhari Copyright © 2014 Tahereh Eftekhari. All rights reserved. A New Double Sequence Space Defined by a Double Sequence of Modulus Functions Tue, 11 Feb 2014 13:29:52 +0000 http://www.hindawi.com/journals/ijanal/2014/684512/ In this work we introduce new spaces of double sequences defined by a double sequence of modulus functions, and we study some properties of this space. Birsen Sağır, Cenap Duyar, and Oğuz Oğur Copyright © 2014 Birsen Sağır et al. All rights reserved. On Compactness of Embeddings of Fourier-Lebesgue Spaces into Modulation Spaces Wed, 18 Dec 2013 12:40:18 +0000 http://www.hindawi.com/journals/ijanal/2013/681573/ It is shown that, for a certain range of parameters, embeddings of Fourier-Lebesgue spaces into modulation spaces are compact. Yevgeniy V. Galperin Copyright © 2013 Yevgeniy V. Galperin. All rights reserved. Normal Families concerning Polynomials and Shared Values Mon, 28 Oct 2013 15:00:24 +0000 http://www.hindawi.com/journals/ijanal/2013/451468/ We study the problem of normal families of meromorphic functions concerning polynomials and shared values. We prove that a family of meromorphic functions in a domain D is normal if, for each function , , where is a polynomial with the origin as zero, is a positive integer, and , are two finite constants. Xin-Li Wang and Ning Cui Copyright © 2013 Xin-Li Wang and Ning Cui. All rights reserved. -Convergence in the Topology Induced by Random 2-Normed Spaces Tue, 16 Jul 2013 10:44:17 +0000 http://www.hindawi.com/journals/ijanal/2013/451762/ We study -convergence which is common generalization of the -convergence of sequences in the topology induced by random 2-normed spaces and prove some important results. U. Yamancı and M. Gürdal Copyright © 2013 U. Yamancı and M. Gürdal. All rights reserved. Common Fixed Point Theorems Using the E.A. and CLR Properties in 2-Menger Spaces Mon, 27 May 2013 12:12:03 +0000 http://www.hindawi.com/journals/ijanal/2013/934738/ First, we prove a common fixed point theorem using weakly compatible maps in 2-Menger space with t-norm of Hadzic type. Second, we prove a common fixed point theorem using the E.A. property along with weakly compatible maps. Further, we obtained a common fixed point theorem using the CLR property along with weakly compatible maps. At the end, we provide an application of our main theorem for four finite families of mappings. Balbir Singh, Vishal Gupta, and Sanjay Kumar Copyright © 2013 Balbir Singh et al. All rights reserved. Generalized Abel Inversion Using Extended Hat Functions Operational Matrix Sun, 19 May 2013 08:49:15 +0000 http://www.hindawi.com/journals/ijanal/2013/652541/ Abel type integral equations play a vital role in the study of compressible flows around axially symmetric bodies. The relationship between emissivity and the measured intensity, as measured from the outside cylindrically symmetric, optically thin extended radiation source, is given by this equation as well. The aim of the present paper is to propose a stable algorithm for the numerical inversion of the following generalized Abel integral equation: , , , using our newly constructed extended hat functions operational matrix of integration, and give an error analysis of the algorithm. The earlier numerical inversions available for the above equation assumed either or . Manoj P. Tripathi, Ram K. Pandey, Vipul K. Baranwal, and Om P. Singh Copyright © 2013 Manoj P. Tripathi et al. All rights reserved. Fractal Spherical Harmonics Mon, 13 May 2013 12:03:27 +0000 http://www.hindawi.com/journals/ijanal/2013/927368/ This paper tackles the construction of fractal maps on the unit sphere. The functions defined are a generalization of the classical spherical harmonics. The methodology used involves an iterated function system and a linear and bounded operator of functions on the sphere. For a suitable choice of the coefficients of the system, one obtains classical maps on the sphere. The different values of the system parameters provide Bessel sequences, frames, and Riesz fractal bases for the Lebesgue space of the square integrable functions on the sphere. The Laplace series expansion is generalized to a sum in terms of the new fractal mappings. M. A. Navascués Copyright © 2013 M. A. Navascués. All rights reserved. On Common Random Fixed Points of a New Iteration with Errors for Nonself Asymptotically Quasi-Nonexpansive Type Random Mappings Wed, 08 May 2013 09:15:37 +0000 http://www.hindawi.com/journals/ijanal/2013/312685/ We prove some strong convergence of a new random iterative scheme with errors to common random fixed points for three and then nonself asymptotically quasi-nonexpansive-type random mappings in a real separable Banach space. Our results extend and improve the recent results in Kiziltunc, 2011, Thianwan, 2008, Deng et al., 2012, and Zhou and Wang, 2007 as well as many others. R. A. Rashwan, P. K. Jhade, and Dhekra Mohammed Al-Baqeri Copyright © 2013 R. A. Rashwan et al. All rights reserved. Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems Thu, 02 May 2013 10:08:04 +0000 http://www.hindawi.com/journals/ijanal/2013/763261/ The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008). As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008). We also furnish some illustrative examples to support our main results. Mohammad Imdad and Sunny Chauhan Copyright © 2013 Mohammad Imdad and Sunny Chauhan. All rights reserved. Regularity Criteria for a Coupled Navier-Stokes and Q-Tensor System Sat, 27 Apr 2013 15:34:14 +0000 http://www.hindawi.com/journals/ijanal/2013/718173/ We study a system describing the evolution of a nematic liquid crystal flow. The system couples a forced Navier-Stokes system describing the flow with a parabolic-type system describing the evolution of the nematic crystal director fields (Q-tensors). We prove some regularity criteria for the local strong solutions. However, we do not provide estimates on the rates of increase of high norms. Jishan Fan and Tohru Ozawa Copyright © 2013 Jishan Fan and Tohru Ozawa. All rights reserved. Universality Properties of a Double Series by the Generalized Walsh System Mon, 22 Apr 2013 08:07:54 +0000 http://www.hindawi.com/journals/ijanal/2013/424686/ We consider a question on existence of a double series by the generalized Walsh system, which is universal in weighted spaces. In particular, we construct a weighted function and a double series by generalized Walsh system of the form with the for all , which is universal in concerning subseries with respect to convergence, in the sense of both spherical and rectangular partial sums. Sergo A. Episkoposian Copyright © 2013 Sergo A. Episkoposian. All rights reserved.