International Journal of Analysis The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Influence of the Center Condition on the Two-Step Secant Method Sun, 24 Sep 2017 00:00:00 +0000 The aim of this paper is to present a new improved semilocal and local convergence analysis for two-step secant method to approximate a locally unique solution of a nonlinear equation in Banach spaces. This study is important because starting points play an important role in the convergence of an iterative method. We have used a combination of Lipschitz and center-Lipschitz conditions on the Fréchet derivative instead of only Lipschitz condition. A comparison is established on different types of center conditions and the influence of our approach is shown through the numerical examples. In comparison to some earlier study, it gives an improved domain of convergence along with the precise error bounds. Finally, some numerical examples including nonlinear elliptic differential equations and integral equations validate the efficacy of our approach. Abhimanyu Kumar, D. K. Gupta, and Shwetabh Srivastava Copyright © 2017 Abhimanyu Kumar et al. All rights reserved. Comment on “Some Congruence Properties of a Restricted Bipartition Function ” Thu, 13 Jul 2017 06:50:56 +0000 Qing Zou Copyright © 2017 Qing Zou. All rights reserved. Best Proximity Point Results for Some Contractive Mappings in Uniform Spaces Wed, 26 Apr 2017 00:00:00 +0000 We introduce the concept of -distance (an analogue of -metric), -proximal contraction, and -proximal cyclic contraction for non-self-mappings in Hausdorff uniform spaces. We investigate the existence and uniqueness of best proximity points for these modified contractive mappings. The results obtained extended and generalised some fixed and best proximity points results in literature. Examples are given to validate the main results. Victoria Olisama, Johnson Olaleru, and Hudson Akewe Copyright © 2017 Victoria Olisama et al. All rights reserved. Geraghty Type Generalized -Contractions and Related Applications in Partial -Metric Spaces Wed, 15 Mar 2017 00:00:00 +0000 The purpose of this paper is to introduce new concepts of -admissible Geraghty type generalized -contraction and to prove that some fixed point results for such mappings are in the perspective of partial -metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphic -contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partial -metric space. Moreover, some examples are presented to illustrate the usability of the new theory. Deepak Singh, Varsha Chauhan, and R. Wangkeeree Copyright © 2017 Deepak Singh et al. All rights reserved. A Characterization of Bi-Jordan Homomorphisms on Banach Algebras Tue, 31 Jan 2017 00:00:00 +0000 For Banach algebras and , we show that if is unital and commutative, each bi-Jordan homomorphism from into a semisimple commutative Banach algebra is a bihomomorphism. Abbas Zivari-Kazempour Copyright © 2017 Abbas Zivari-Kazempour. All rights reserved. Stability and Boundedness of Solutions to a Certain Second-Order Nonautonomous Stochastic Differential Equation Sun, 25 Dec 2016 08:59:37 +0000 This paper focuses on stability and boundedness of certain nonlinear nonautonomous second-order stochastic differential equations. Lyapunov’s second method is employed by constructing a suitable complete Lyapunov function and is used to obtain criteria, on the nonlinear functions, that guarantee stability and boundedness of solutions. Our results are new; in fact, according to our observations from the relevant literature, this is the first attempt on stability and boundedness of solutions of second-order nonlinear nonautonomous stochastic differential equations. Finally, examples together with their numerical simulations are given to authenticate and affirm the correctness of the obtained results. A. T. Ademola, S. Moyo, B. S. Ogundare, M. O. Ogundiran, and O. A. Adesina Copyright © 2016 A. T. Ademola et al. All rights reserved. Construction and Analysis of Binary Subdivision Schemes for Curves and Surfaces Originated from Chaikin Points Tue, 06 Dec 2016 14:28:17 +0000 We present a new variant of Lane-Riesenfeld algorithm for curves and surfaces both. Our refining operator is the modification of Chaikin/Doo-Sabin subdivision operator, while each smoothing operator is the weighted average of the four/sixteen adjacent points. Our refining operator depends on two parameters (shape and smoothing parameters). So we get new families of univariate and bivariate approximating subdivision schemes with two parameters. The bivariate schemes are the nontensor product schemes for quadrilateral meshes. Moreover, we also present analysis of our families of schemes. Furthermore, our schemes give cubic polynomial reproduction for a specific value of the shape parameter. The nonuniform setting of our univariate and bivariate schemes gives better performance than that of the uniform schemes. Rabia Hameed and Ghulam Mustafa Copyright © 2016 Rabia Hameed and Ghulam Mustafa. All rights reserved. Some New Ostrwoski’s Inequalities for Functions Whose th Derivatives Are -Convex Mon, 28 Nov 2016 13:41:13 +0000 We prove some new Ostrowski’s inequalities for functions whose th derivatives are -convex. Badreddine Meftah Copyright © 2016 Badreddine Meftah. All rights reserved. Coefficient Estimates for Certain Subclasses of Biunivalent Functions Defined by Convolution Tue, 22 Nov 2016 14:36:34 +0000 We introduce two new subclasses of the function class of biunivalent functions in the open disc defined by convolution. Estimates on the coefficients and for the two subclasses are obtained. Moreover, we verify Brannan and Clunie’s conjecture for our subclasses. R. Vijaya, T. V. Sudharsan, and S. Sivasubramanian Copyright © 2016 R. Vijaya et al. All rights reserved. Multiplicity of Solutions for Schrödinger Equations with Concave-Convex Nonlinearities Tue, 22 Nov 2016 09:39:02 +0000 We study the multiplicity of solutions for a class of semilinear Schrödinger equations: where satisfies some kind of coercive condition and involves concave-convex nonlinearities with indefinite signs. Our theorems contain some new nonlinearities. Dong-Lun Wu, Chun-Lei Tang, and Xing-Ping Wu Copyright © 2016 Dong-Lun Wu et al. All rights reserved. A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus Tue, 22 Nov 2016 09:32:28 +0000 This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table. Also, some geometric interpretations of convex functions are presented with respect to the non-Newtonian slope. Finally, using multiplicative continuous convex functions we give an application. Uğur Kadak and Yusuf Gürefe Copyright © 2016 Uğur Kadak and Yusuf Gürefe. All rights reserved. Strong -Convexity and Separation Theorems Thu, 10 Nov 2016 11:15:46 +0000 Jensen inequality for strongly -convex functions and a characterization of pairs of functions that can be separated by a strongly -convex function are presented. As a consequence, a stability result of the Hyers-Ulam type is obtained. Teodoro Lara, Nelson Merentes, and Kazimierz Nikodem Copyright © 2016 Teodoro Lara et al. All rights reserved. Straightforward Proofs of Ostrowski Inequality and Some Related Results Wed, 09 Nov 2016 09:39:22 +0000 We give proofs of some known results in very simple and antique way. Also we find some general bounds of a nonnegative difference of the Hadamard inequality and an Ostrowski-Grüss type inequality is proved. Ghulam Farid Copyright © 2016 Ghulam Farid. All rights reserved. On the Marginal Distribution of the Diagonal Blocks in a Blocked Wishart Random Matrix Tue, 01 Nov 2016 06:27:22 +0000 Let be a blocked Wishart random matrix with diagonal blocks of orders and . The goal of the paper is to find the exact marginal distribution of the two diagonal blocks of . We find an expression for this marginal density involving the matrix-variate generalized hypergeometric function. We became interested in this problem because of an application in spatial interpolation of random fields of positive definite matrices, where this result will be used for parameter estimation, using composite likelihood methods. Kjetil B. Halvorsen, Victor Ayala, and Eduardo Fierro Copyright © 2016 Kjetil B. Halvorsen et al. All rights reserved. Inclusion of the Generalized Bessel Functions in the Janowski Class Thu, 27 Oct 2016 12:27:22 +0000 Sufficient conditions on , , , , and are determined that will ensure the generalized Bessel function satisfies the subordination . In particular this gives conditions for , , to be close-to-convex. Also, conditions for to be Janowski convex and to be Janowski starlike in the unit disk are obtained. Saiful R. Mondal and Mohammed Al Dhuain Copyright © 2016 Saiful R. Mondal and Mohammed Al Dhuain. All rights reserved. Hermite-Hadamard Type Inequalities Obtained via Fractional Integral for Differentiable -Convex and -Convex Functions Thu, 20 Oct 2016 06:51:24 +0000 Some Hermite-Hadamard type inequalities involving fractional integrals for -convex and ()-convex functions are obtained. Erhan Set, Süleyman Sami Karataş, and Muhammad Adil Khan Copyright © 2016 Erhan Set et al. All rights reserved. Common Fixed Point Results for Six Mappings via Integral Contractions with Applications Wed, 19 Oct 2016 07:14:20 +0000 Common fixed point theorems for six self-mappings under integral type inequality satisfying and properties in the context of complex valued metric space (not necessarily complete) are established. The derived results are new even for ordinary metric spaces. We prove existence result for optimal unique solution of the system of functional equations used in dynamical programming with complex domain. Mian Bahadur Zada, Muhammad Sarwar, and Nayyar Mehmood Copyright © 2016 Mian Bahadur Zada et al. All rights reserved. Some Nonlinear Stochastic Cauchy Problems with Generalized Stochastic Processes Tue, 18 Oct 2016 13:38:27 +0000 We study some nonlinear stochastic Cauchy problems in the framework of the -algebras. We adapt the definitions to this framework. By means of suitable regularizations, we define associated generalized problems. We use our previous results about the wave equation in canonical form to obtain generalized solutions. We compare the generalized solutions with the classical ones when they exist. Victor Dévoué Copyright © 2016 Victor Dévoué. All rights reserved. Hyers-Ulam Stability of Fractional Nabla Difference Equations Wed, 21 Sep 2016 11:42:44 +0000 We investigate the Hyers-Ulam stability, the generalized Hyers-Ulam stability, and the -Hyers-Ulam stability of a linear fractional nabla difference equation using discrete Laplace transform. We provide a few examples to illustrate the applicability of established results. Jagan Mohan Jonnalagadda Copyright © 2016 Jagan Mohan Jonnalagadda. All rights reserved. On Faster Implicit Hybrid Kirk-Multistep Schemes for Contractive-Type Operators Mon, 19 Sep 2016 14:22:04 +0000 The purpose of this paper is to prove strong convergence and T-stability results of some modified hybrid Kirk-Multistep iterations for contractive-type operator in normed linear spaces. Our results show through analytical and numerical approach that the modified hybrid schemes are better in terms of convergence rate than other hybrid Kirk-Multistep iterative schemes in the literature. O. T. Wahab and K. Rauf Copyright © 2016 O. T. Wahab and K. Rauf. All rights reserved. Variational-Like Inequalities for Weakly Relaxed Pseudomonotone Set-Valued Mappings in Banach Space Wed, 07 Sep 2016 16:45:04 +0000 We introduce and study variational-like inequalities for generalized pseudomonotone set-valued mappings in Banach spaces. By using KKM technique, we obtain the existence of solutions for variational-like inequalities for generalized pseudomonotone set-valued mappings in reflexive Banach spaces. The results presented in this paper are generalizations and improvements of the several well-known results in the literature. Syed Shakaib Irfan and Mohammad Firdosh Khan Copyright © 2016 Syed Shakaib Irfan and Mohammad Firdosh Khan. All rights reserved. Retracted: Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces Sun, 21 Aug 2016 06:32:42 +0000 International Journal of Analysis Copyright © 2016 International Journal of Analysis. All rights reserved. Some Congruence Properties of a Restricted Bipartition Function Mon, 08 Aug 2016 07:54:11 +0000 Let denote the number of bipartitions of a positive integer subject to the restriction that each part of is divisible by . In this paper, we prove some congruence properties of the function for , 11, and , for any integer , by employing Ramanujan’s theta-function identities. Nipen Saikia and Chayanika Boruah Copyright © 2016 Nipen Saikia and Chayanika Boruah. All rights reserved. On Inclusion Relations between Some Sequence Spaces Wed, 03 Aug 2016 08:06:15 +0000 We determine the relations between the classes of almost -statistically convergent sequences and the relations between the classes of strongly almost -summable sequences for various sequences , in the class . Furthermore we also give the relations between the classes of almost -statistically convergent sequences and the classes of strongly almost -summable sequences for various sequences . R. Çolak, Ç. A. Bektaş, H. Altınok, and S. Ercan Copyright © 2016 R. Çolak et al. All rights reserved. Fixed Point Theorems for Geraghty Type Contractive Mappings and Coupled Fixed Point Results in 0-Complete Ordered Partial Metric Spaces Wed, 03 Aug 2016 07:47:41 +0000 We establish new fixed point theorems in 0-complete ordered partial metric spaces. Also, we give remark on coupled generalized Banach contraction. Some examples illustrate the usability of our results. The theorems presented in this paper are generalizations and improvements of the several well known results in the literature. Esra Yolacan Copyright © 2016 Esra Yolacan. All rights reserved. On a Fixed Point Theorem with Application to Integral Equations Mon, 30 May 2016 08:48:12 +0000 We introduce the notion of dualistic Geraghty’s type contractions. We prove some fixed point theorems for ordered mappings satisfying the abovementioned contractions. We discuss an application of our fixed point results to show the existence of solution of integral equations. Muhammad Nazam and Muhammad Arshad Copyright © 2016 Muhammad Nazam and Muhammad Arshad. All rights reserved. Singular Differential Equations and -Drazin Invertible Operators Tue, 15 Mar 2016 11:38:07 +0000 We extend results of Favini, Nashed, and Zhao on singular differential equations using the -Drazin inverse and the order of a quasinilpotent operator in the sense of Miekka and Nevanlinna. Two classes of singularly perturbed differential equations are studied using the continuity properties of the -Drazin inverse obtained by Koliha and Rakočević. Alrazi Abdeljabbar and Trung Dinh Tran Copyright © 2016 Alrazi Abdeljabbar and Trung Dinh Tran. All rights reserved. Cyclicity of Special Operators on a BK with AK Space Mon, 21 Dec 2015 11:59:14 +0000 Let be a complex domain and let be a reflexive BK space with AK such that and the functional of evaluation at is bounded for all . We will investigate the cyclicity for the adjoint of a weighted composition operator acting on . Leila Bagheri and Bahmann Yousefi Copyright © 2015 Leila Bagheri and Bahmann Yousefi. All rights reserved. A Survey on Operator Monotonicity, Operator Convexity, and Operator Means Wed, 11 Nov 2015 09:13:36 +0000 This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means. Pattrawut Chansangiam Copyright © 2015 Pattrawut Chansangiam. All rights reserved. Some Ostrowski Type Inequalities for Harmonically -Convex Functions in Second Sense Mon, 26 Oct 2015 12:34:27 +0000 The authors introduce the concept of harmonically -convex functions in second sense and establish some Ostrowski type inequalities of these classes of functions. Imran Abbas Baloch and İmdat İşcan Copyright © 2015 Imran Abbas Baloch and İmdat İşcan. All rights reserved.