Viscosity Approximation Methods for Fixed Points of Asymptotically Nonexpansive Semigroup in Banach Space

A composite explicit iterative process with a viscosity method for Lipschitzian semigroup in a smooth Banach space

Viscosity Approximation of Common Fixed Points for L-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces

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...

Viscosity Approximation Methods for Fixed Points of Asymptotically Nonexpansive Mappings in Banach Space

In this paper, under the framework of Banach space with uniformly Gateaux differentiable norm and uniform normal structure, we use the existence theorem of fixed points of Li and Sims to investigate the convergence of the implicit iteration process and the explicit iteration process for asymptotically nonexpansive mappings. We get the convergence theorems.

Stability and convergence theorems of pointwise asymptotically nonexpansive random operator in Banach space

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.

Convergence theorems of multi-step iterative algorithm with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces

The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).