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, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W -mappings of a countable family of ...

We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lips...

It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

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...

begin{abstract} In this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable Banach space. end{abstract}

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.