Abstract In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied uniformly convex 2-uniformly smooth real Banach space with Opial property best smoothness constant κ satisfying condition $0&lt;\kappa &lt; \frac{1}{\sqrt{2}}$ <mml:math xmlns:mml="http://ww...

We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi’s hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is pr...

the purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. the results in this paper improve and extend the corresponding results of xu and ori, zhou and chang, sun, yang and yu in some aspects.

CONVERGENCE ANALYSIS OF AN ITERATION SCHEME FOR LIPSCHITZ STRONGLY PSEUDOCONTRACTIVE MAPPINGS Shin Min Kang Department of Mathematics, Gyeongsang National University, Jinju 660-701, KOREA [email protected] Arif Rafiq Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan [email protected] ABSTRACT In this paper, we establish the strong convergence for the Agarwal et al. [1] ite...

In this paper, strong convergence theorems of Ishikawa type implicit iteration process with errors for a finite family of asymptotically nonexpansive in the intermediate sense and asymptotically quasi-pseudocontractive type mappings in normed linear spaces are established by using a new analytical method, which essentially improve and extend some recent results obtained by Yang [Convergence the...

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767–77...

A new iterative method for equilibrium problems and fixed point problems for infinite family of nonself strictly pseudocontractive mappings Abstract The purpose of this paper is to present an iterative method for finding a common element of the set of solutions for an equilibrium problem and the set of common fixed points for a countably infinite family of nonself λ i-strictly pseudocontractive...

We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach...

The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects.