Received: December 21, 2010 Accepted: January 7, 2011 doi:10.5539/jmr.v3n2p151 Abstract In this paper, we study fixed point theorems for multi-valued weak contractions. We show that the Picard projection iteration converges to a fixed point, give a rate of convergence and generalize Collage theorem. This work includes results on multi-valued contraction mappings studied by (Kunze, H.E., La Torr...

In this paper, we proposed a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two total asymptotically nonexpansive non-self mappings and establish some weak convergence theorems for mentioned scheme and mappings in the setting of uniformly convex Banach spaces. Our results extend and generalize several results from the current existing li...

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...

In this paper, based on a generalized projection, we introduce a new modified Halpern-type iteration algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of a common fixed point of an infinitely countable family of relatively quasi-nonexpansive mappings in the framework of Banach spaces. We establish the strong convergence theorem and obtain some ...

In this paper, we introduce two modified Mann-type iterative algorithms for finding a common element of the set of common fixed points of a family of quasi-φ-asymptotically nonexpansive mappings and the set of solutions of an equilibrium problem in Banach spaces. Then we study the strong convergence of the algorithms. Our results improve and extend the corresponding results announced by many ot...

The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-φ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the p...

In this paper, we consider a modified projective algorithm for finding common elements of the set of common fixed points of a finite family of quasi-φ-nonexpansive mappings and the set of solutions of an equilibrium problem in uniformly smooth and strictly convex Banach spaces with the property(K). Our results improve and extend the corresponding results announced by many others. AMS subject cl...

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...