http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Sun, 19 May 2013 08:49:15 +0000 http://www.hindawi.com/journals/analysis/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. Mon, 13 May 2013 12:03:27 +0000 http://www.hindawi.com/journals/analysis/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. Wed, 08 May 2013 09:15:37 +0000 http://www.hindawi.com/journals/analysis/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. Thu, 02 May 2013 10:08:04 +0000 http://www.hindawi.com/journals/analysis/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. Sat, 27 Apr 2013 15:34:14 +0000 http://www.hindawi.com/journals/analysis/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. Mon, 22 Apr 2013 08:07:54 +0000 http://www.hindawi.com/journals/analysis/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. Thu, 11 Apr 2013 15:17:35 +0000 http://www.hindawi.com/journals/analysis/2013/654659/ Recently, Samet et al. (2012) introduced the notion of --contractive type mappings. They established some fixed point theorems for these mappings in complete metric spaces. In this paper, we introduce the notion of a coupled --contractive mapping and give a common fixed point result about the mapping. Also, we give a result of common fixed points of some coupled self-maps on complete metric spaces satisfying a contractive condition. Jalal Hassanzadeasl Copyright © 2013 Jalal Hassanzadeasl. All rights reserved. Wed, 10 Apr 2013 08:59:47 +0000 http://www.hindawi.com/journals/analysis/2013/538027/ We study the uniqueness of meromorphic functions concerning differential polynomials sharing fixed point and obtain some significant results , which improve the results due to Lin and Yi (2004). Subhas S. Bhoosnurmath and Veena L. Pujari Copyright © 2013 Subhas S. Bhoosnurmath and Veena L. Pujari. All rights reserved. Mon, 08 Apr 2013 15:44:02 +0000 http://www.hindawi.com/journals/analysis/2013/736451/ We prove a related fixed point theorem for set-valued mappings in three Menger spaces. Some examples are also furnished to support the results. Our main result generalizes and extends several known results in the literature. Ismat Beg and Sunny Chauhan Copyright © 2013 Ismat Beg and Sunny Chauhan. All rights reserved. Thu, 04 Apr 2013 14:48:52 +0000 http://www.hindawi.com/journals/analysis/2013/404838/ We introduce a condition (W.C.C) and prove a common fixed point theorem for two hybrid pairs of mappings in b-metric spaces. K. P. R. Rao and K. R. K. Rao Copyright © 2013 K. P. R. Rao and K. R. K. Rao. All rights reserved. Wed, 03 Apr 2013 14:19:59 +0000 http://www.hindawi.com/journals/analysis/2013/380938/ We introduce a new class of analytic functions with varying arguments in the open unit disc defined by the Salagean operator. The object of the present paper is to determine coefficient estimates, extreme points, and distortion theorems for functions belonging to the class . M. K. Aouf, A. O. Mostafa, A. Shamandy, and E. A. Adwan Copyright © 2013 M. K. Aouf et al. All rights reserved. Wed, 03 Apr 2013 10:03:32 +0000 http://www.hindawi.com/journals/analysis/2013/749684/ In this paper, we introduce the notions of regularly , -convergence and regularly , -Cauchy double sequence of fuzzy numbers. Also, we study some properties of these concepts. Erdinç Dündar, Özer Talo, and Feyzi Başar Copyright © 2013 Erdinç Dündar et al. All rights reserved. Wed, 27 Mar 2013 15:16:30 +0000 http://www.hindawi.com/journals/analysis/2013/407958/ Our goal in this paper is to give characterizations for some concepts of polynomial stability for variational nonautonomous difference equations. The obtained results can be considered generalizations for the case of variational nonautonomous difference equations of some theorems proved by Barbashin (1967), Datko (1973), and Lyapunov (1992), for evolution operators. Mihail Megan, Traian Ceauşu, and Mihaela Aurelia Tomescu Copyright © 2013 Mihail Megan et al. All rights reserved. Wed, 27 Mar 2013 11:40:34 +0000 http://www.hindawi.com/journals/analysis/2013/397262/ We aim at studying the near subnormality of the unilateral weighted shifts, whose moment sequences are defined by linear recursive relations of finite order. Using the basic properties of recursive sequences, we provide a natural necessary condition, that ensure the near subnormality of this important class of weighted shifs. Some related new results are established; moreover, applications and consequences are presented; notably the notion of near subnormal completion weighted shift is implanted and explored. R. Ben Taher and M. Rachidi Copyright © 2013 R. Ben Taher and M. Rachidi. All rights reserved. Wed, 27 Mar 2013 11:01:40 +0000 http://www.hindawi.com/journals/analysis/2013/486357/ We establish fixed-point theorems for mixed monotone mappings in the setting of ordered metric spaces which satisfy a contractive condition for all points that are related by a given ordering. We also give a global attractivity result for all solutions of the difference equation where satisfies certain monotonicity conditions with respect to the given ordering. As an application of our obtained results, we present some iterative algorithms to solve a class of matrix equations. A numerical example is also presented to test the validity of the algorithms. Mujahid Abbas and Maher Berzig Copyright © 2013 Mujahid Abbas and Maher Berzig. All rights reserved. Sun, 24 Mar 2013 09:15:05 +0000 http://www.hindawi.com/journals/analysis/2013/247378/ We prove the existence theorem of fixed points for a generalized weak contractive mapping in modular spaces. Chirasak Mongkolkeha and Poom Kumam Copyright © 2013 Chirasak Mongkolkeha and Poom Kumam. All rights reserved. Wed, 20 Mar 2013 10:21:28 +0000 http://www.hindawi.com/journals/analysis/2013/259418/ Here, we prove the existence of -nondecreasing solution to a nonlinear quadratic integral equation of Urysohn type by applying the technique of weak noncompactness. Also, the asymptotic stability of solutions for that quadratic integral equation is studied. H. H. G. Hashem and A. R. Al-Rwaily Copyright © 2013 H. H. G. Hashem and A. R. Al-Rwaily. All rights reserved. Tue, 19 Mar 2013 18:34:42 +0000 http://www.hindawi.com/journals/analysis/2013/710358/ A generalized fractional differintegral operator is used to define some new subclasses of analytic functions in the open unit disk . For each of these new function classes, several inclusion relationships are established. Amit Soni and Shashi Kant Copyright © 2013 Amit Soni and Shashi Kant. All rights reserved. Tue, 19 Mar 2013 18:08:44 +0000 http://www.hindawi.com/journals/analysis/2013/307234/ We obtain sufficient conditions for the existence of unique common fixed point of -weakly contractive mappings on complete rectangular metric spaces. In the process, we generalize several fixed point results from the literature. We also give an example to illustrate our work. Muhammad Arshad, Jamshaid Ahmad, and Erdal Karapınar Copyright © 2013 Muhammad Arshad et al. All rights reserved. Thu, 14 Mar 2013 15:16:19 +0000 http://www.hindawi.com/journals/analysis/2013/512372/ The fundamental aim of this paper is to introduce and investigate a new property of a quasi-2-normed space based on a question given by Park (2006) for the completion quasi-2-normed space. Finally, we also find an answer for Park's question. Mehmet Kır and Mehmet Acikgoz Copyright © 2013 Mehmet Kır and Mehmet Acikgoz. All rights reserved. Wed, 13 Mar 2013 14:32:03 +0000 http://www.hindawi.com/journals/analysis/2013/368150/ We report the finding of the simple nonlinear autonomous system exhibiting infinite-scroll attractor. The system is generated from the pendulum equation with complex-valued function. The proposed system is having infinitely many saddle points of index two which are responsible for the infinite-scroll attractor. Sachin Bhalekar Copyright © 2013 Sachin Bhalekar. All rights reserved. Tue, 12 Mar 2013 13:14:29 +0000 http://www.hindawi.com/journals/analysis/2013/172813/ We use the Calogero equation to illustrate the following two aspects of the Painlevé analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painlevé test for integrability, the singular expansions of its solutions around characteristic hypersurfaces can be neither single-valued functions of independent variables nor single-valued functionals of data. Second, if the truncation of singular expansions of solutions is consistent, the truncation not necessarily leads to the simplest, or elementary, auto-Bäcklund transformation related to the Lax pair. Sergei Sakovich Copyright © 2013 Sergei Sakovich. All rights reserved. Tue, 12 Mar 2013 09:26:23 +0000 http://www.hindawi.com/journals/analysis/2013/126163/ The sequence space was introduced and studied by Mursaleen (1983). In this article we introduce the sequence space 2 and study some of its properties and inclusion relations. Vakeel A. Khan and Nazneen Khan Copyright © 2013 Vakeel A. Khan and Nazneen Khan. All rights reserved. Sun, 10 Mar 2013 15:31:04 +0000 http://www.hindawi.com/journals/analysis/2013/878051/ This work is concerned with the mathematical analysis of a model proposed by Gatenby and Gawlinski (1996) in order to support the hypothesis that tumor-induced alteration of microenvironmental pH may provide a simple but comprehensive mechanism to explain cancer invasion. We give an intuitive proof for the existence of a solution under general initial conditions upon using an iterative approach. Numerical simulations are also performed, which endorse the predictions of the model when compared with experimentally observed qualitative facts. Christian Märkl, Gülnihal Meral, and Christina Surulescu Copyright © 2013 Christian Märkl et al. All rights reserved. Wed, 06 Mar 2013 09:02:00 +0000 http://www.hindawi.com/journals/analysis/2013/852727/ Existence and uniqueness of fixed points are established for a mapping satisfying a contractive condition involving a rational expression on a generalized metric space. Several particular cases and applications as well as some illustrative examples are given. Jamshaid Ahmad, Muhammad Arshad, and Calogero Vetro Copyright © 2013 Jamshaid Ahmad et al. All rights reserved. Thu, 21 Feb 2013 11:48:15 +0000 http://www.hindawi.com/journals/analysis/2013/328032/ A general class of the 2-variable polynomials is considered, and its properties are derived. Further, these polynomials are used to introduce the 2-variable general-Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established. The differential equation, recurrence relations, and other properties for the 2VgAP are obtained within the context of the monomiality principle. This paper is the first attempt in the direction of introducing a new family of special polynomials, which includes many other new special polynomial families as its particular cases. Subuhi Khan and Nusrat Raza Copyright © 2013 Subuhi Khan and Nusrat Raza. All rights reserved. Thu, 07 Feb 2013 09:16:59 +0000 http://www.hindawi.com/journals/analysis/2013/723698/ We give a simple method for applying ordinary differential equation to solve the nonlinear generalized Camassa-Holm equation . Furthermore we give a new ansätz. In the cases where , the numerical simulations demonstrate the results. Lei Zhang and Xing Tao Wang Copyright © 2013 Lei Zhang and Xing Tao Wang. All rights reserved. Wed, 06 Feb 2013 11:52:44 +0000 http://www.hindawi.com/journals/analysis/2013/926340/ We study the uniqueness of meromorphic functions that share one small function with more general differential polynomial . As corollaries, we obtain results which answer open questions posed by Yu (2003). Subhas S. Bhoosnurmath and Smita R. Kabbur Copyright © 2013 Subhas S. Bhoosnurmath and Smita R. Kabbur. All rights reserved. Tue, 05 Feb 2013 11:23:12 +0000 http://www.hindawi.com/journals/analysis/2013/153128/ We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered. R. M. El-Ashwah, M. K. Aouf, A. A. M. Hassan, and A. H. Hassan Copyright © 2013 R. M. El-Ashwah et al. All rights reserved. Mon, 04 Feb 2013 09:43:20 +0000 http://www.hindawi.com/journals/analysis/2013/726387/ Cyclic weaker-type contraction conditions involving a generalized control function (with two variables) are used for mappings on 0-complete partial metric spaces to obtain fixed point results, thus generalizing several known results. Various examples are presented showing how the obtained theorems can be used and that they are proper extensions of the known ones. Hemant Kumar Nashine and Zoran Kadelburg Copyright © 2013 Hemant Kumar Nashine and Zoran Kadelburg. All rights reserved.