the notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $cat(0)$ space, where the curvature is bounded from above by zero. in fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. in this paper, w...

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

with kn ≥ 0, rn ≥ 0, kn → 1, rn → 0 n → ∞ , for each x, y ∈ C, n 0, 1, 2, . . . . If kn 1 and rn 0, 1.1 reduces to nonexpansive mapping; if rn 0, 1.1 reduces to asymptotically nonexpansive mapping; if kn 1, 1.1 reduces to asymptotically nonexpansive-type mapping. So, a generalized asymptotically nonexpansive mapping is much more general than many other mappings. Browder 1 introduced the followi...

for all x ∈ C, p ∈ F T and n ≥ 1. It is clear that if F T is nonempty, then the asymptotically nonexpansive mapping, the asymptotically quasi-nonexpansive mapping, and the generalized quasi-nonexpansive mapping are all the generalized asymptotically quasi-nonexpansive mapping. Recall also that a mapping T : C → C is said to be asymptotically quasi-nonexpasnive in the intermediate sense provided...

Recently, Chang, et al introduce the concept of total asymptotically nonexpansive mapping which contain the asymptotically nonexpansive mapping. The purpose of the paper is to analyze a three-step iterative scheme for total asymptotically nonexpansive mapping in uniformly convex hyperbolic spaces. Meanwhile, we obtain a ∆-convergence theorem of the three-step iterative scheme for total asymptot...

We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study...

in this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regularasymptotically nonexpansive mappings in a real reflexive banach space with a uniformly g$hat{a}$teaux differentiable norm. our result is applicable in $l_{p}(ell_{p})$ spaces,$1 < p

In this article, we consider an implicit iterative scheme for two asymptotically quasi-I-nonexpansive mappingsS1, S2 and two asymptotically quasi-nonexpansive mapping I1, I2 in Banach space. We obtain convergence results for considered iteration to common fixed point of two asymptotically quasi-I-nonexpansive mappings, asymptotically quasi-nonexpansive mapping and equilibrium problem in frame w...

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...