We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly nonexpansive mappings is nearly equal to the average of the ranges of the mappings. A striking application of this result yields that the average of asymptotically r...

Citation: Reich S and Zaslavski AJ (2015) Generic convergence of infinite products of nonexpansive mappings with unbounded domains. We study the generic convergence of infinite products of nonexpansive mappings with unbounded domains in hyperbolic metric spaces.

The main purpose of this paper is to study an iteration procedure for finding a common fixed point of a countable family of nonexpansive mappings in Banach spaces. We introduce a Mann type iteration procedure. Then we prove that such a sequence converges weakly to a common fixed point of a countable family of nonexpansive mappings. Moreover, we apply our result to the problem of finding a commo...

In this article, we introduce a new general iterative method for finding a common element of the set of solutions generalized for mixed equilibrium problems, the set of solution for fixed point for nonexpansive mappings and the set of solutions for the variational inclusions for b1, b2-inverse-strongly monotone mappings in a real Hilbert space. We prove that the sequence converges strongly to a...

We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically I-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by C. E. Chidume and E. U. Ofoedu, 2009 . We construct examples of total asymptotically nonexpansive mappings which are not asym...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

The aim of this paper is to prove a new iterative sequence {xn} under some sufficient and necessary conditions converges strongly to a common fixed point of asymptotically nonexpansive mappings {Ti}i=1 by using viscosity approximation methods. Our results extend and improve some recent results. Mathematics Subject Classification: 47H09, 47H10

In this paper, we extend the results of Inprasit and Wattanataweekul [7] to the class of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense. We prove some strong convergence theorems for asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense using a three-step iterative method for finding a common element of the set of solutions of a generalized m...