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In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51–60] and Benavides et al. [Math. Nachr. 248(2003), 62–71]. [ABSTRACT FROM AUTHOR]

This paper studies the drive-response synchronization for quaternion-valued shunting inhibitory cellular neural networks (QVSICNNs) with mixed delays. First, QVSICNN is decomposed into an equivalent real-valued system in order to avoid the non-commutativity of the multiplicity. Then, the existence of almost periodic solutions is obtained based on the Banach fixed point theorem. An novel state-feedback controller is designed to ensure the global exponential almost periodic synchronization. At the end of the paper, an example is given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, by using the Banach fixed point theorem, we prove the existence and uniqueness theorem of a fractional Volterra integral equation in the space of Lebesgue integrableL1(R+) on unbounded interval [0,∞). [ABSTRACT FROM AUTHOR]

In this paper we investigate the stability and asymptotic stability of the zero solution for the first order delay differential equation þ(t)=-ΣNj=1(t)y(t-τj(t))+f(t,y(t-964;(t)) where the delay is variable and by using Banach fixed point theorem. We give new conditions to ensure the stability and asymptotic stability of the zero solution of this equation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the additive (α, β)-functional equation ... for all complex numbers α with [α] D 1 and for a fixed nonzero complex number β. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (α, β)-functional equation (0.1) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

Let (X, d) be a complete metric space and T: X→X a mapping of X. In 1975 Dass and Gupta introduced the following rational type contractive condition to prove a generalization of Banach's Fixed Point Theorem: For α, β∈ [0, 1), such that α + β < 1, we have ∀x, y ∈ X, d(Tx, Ty) ≤ α d(y, Ty)(1 +d(x, Tx)) / 1 + d(x, y) + βd(x, y), where T is continuous. There are several generalization and extension of Dass and Gupta’s result under the hypothesis that T is continuous and α + β < 1. In this paper, we prove some fixed point theorems in a complete metric space setting by employing more general rational type contractive conditions than the above one. We show in our results that the continuity of the above operator T is unnecessary and the restrictive condition that α + β < 1 is also removed. Our results generalize and extend those of Das and Gupta and several known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider an iterative procedure for approximating common fixed points of two generalized asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.This will extend the results of Cholamjiak and Suantai, Khan and those generalized therein to the case of generalized asymptotically quasi-nonexpansive mappings and by a faster iterative procedure. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce a new hybrid iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, set of common fixed points of a family of quasi-φ-asymptotically nonexpansive mappings, and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. The results presented in the paper improve and extend the corresponding results announced by some authors. [ABSTRACT FROM AUTHOR]

In this paper, we consider a set-valued implicit quasi-variational inequality problem in real uniformly smooth Banach space and show its equivalence with a fixed-point problem. Using this equivalence and Banach contraction principle for set-valued mapping, we prove the existence of solution for the set-valued implicit quasi-variational inequality problem. Further, we propose and analyze an iterative algorithm for the set-valued implicit quasi-variational inequality problem and discuss its convergence analysis and stability. The theorems presented in this paper generalize, improve and unify the results given in Noor [20,22] and the references therein. [ABSTRACT FROM AUTHOR]

Abstract: W.V. Petryshyn [Remark on condensing and -set-contractive mappings, J. Math. Anal. Appl. 39 (1972) 717–741] and R.D. Nussbaum [Degree theory for local condensing maps, J. Math. Anal. Appl. 37 (1972) 741–766] defined the topological degree of 1-set-contractive fields and studied fixed point theorems of 1-set-contractive operators by virtue of the potential tool. Following them, G.Z. Li [The fixed point index and the fixed point theorems of 1-set-contraction mappings, Proc. Amer. Math. Soc. 104 (1988) 1163–1170] introduced the concept of semi-closed 1-set-contractive operators and studied the fixed point theorems for such a class of operators. In this paper, we continue to study semi-closed 1-set-contractive operators and investigate the boundary conditions under which the topological degrees of 1-set-contractive fields, , are equal to 1. Correspondingly, we can obtain some new fixed point theorems for 1-set-contractive operators which improve and extend many famous theorems such as the Leray–Schauder theorem, Rothe’s theorem, Altman’s theorem, Petryshyn’s theorem, etc. On the other hand, this class of 1-set-contractive operators includes strict set-contractive operators, condensing operators, semi-contractive operators and others (see [G.Z. Li, The fixed point index and the fixed point theorems of 1-set-contraction mappings, Proc. Amer. Math. Soc. 104 (1988) 1163–1170; L.S. Liu, Approximation theorems and fixed point theorems for various class of 1-set-contractive mappings in Banach spaces, Acta Math. Sinica 17 (2001) 103–112]). So the results in this paper remain valid for the above-mentioned operators. In addition, our conclusions and methods are different from the ones in many recent works (see [L.S. Liu, Approximation theorems and fixed point theorems for various class of 1-set-contractive mappings in Banach spaces, Acta Math. Sinica 17 (2001) 103–112; N. Shahzad, S. Latif, Random fixed points for several classes of 1-ball-contractive and 1-set-contractive random maps, J. Math. Anal. Appl. 237 (1999) 83–92; T.C. Lin, Random approximations and random fixed point theorems for continuous 1-set-contractive random maps, Proc. Amer. Math. Soc. 123 (1995) 1167–1176]). [Copyright &y& Elsevier]

By processing the problem through fixed point theory and propagator theory, we investigate the periodicity of solutions to a class of impulsive evolution equations in Hilbert spaces and establish some existence theorems for periodic solutions. Moreover, the asymptotic stability of periodic solutions is obtained under suitable conditions. As one will see, the concept of an impulsive propagator is introduced for the first time in the paper. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the second-order three-point boundary value problem in a Banach space , where is the zero element of . By using the Sadovskii fixed point theorem, we get the existence of at least one (positive) solution. As an application, we give an example to demonstrate our results. [Copyright &y& Elsevier]

The article provides an overview of the study which examines the locally uniform nonsquare in generalized Cesàro sequence spaces. It found that the generalized Cesàro sequence spaces possessed the locally uniform nonsquare and have the fixed point property, but they are not uniformly nonsquare. It specified that the result is related to the result of the paper J. False and colleagues in 2006. It was done through giving examples and the motivation to find the geometric properties that are weaker than uniformly nonsquare, but still possessed the fixed point property in any Banach spaces .

In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result. [ABSTRACT FROM AUTHOR]

A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991). [ABSTRACT FROM AUTHOR]