Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces

Wei-Wei Lin,Jin-Ping Wang,Liang-Gen Hu

doi:10.1155/2010/150539

Abstract

The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to -strict pseudocontractions in -uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm. The main result improves and extends many nice results existing in the current literature.

Highlights

Let E be a real Banach space, and let C be a nonempty closed convex subset E
In 2007, Marino and Xu 2 showed that the Mann iterative sequence converges weakly to a fixed point of λ-strict pseudocontractions in Hilbert spaces
Hu and Wang 4 obtained that the Mann iterative sequence converges weakly to a fixed point of λ-strict pseudocontractions with respect to p in p-uniformly convex Banach spaces

Summary

Introduction

Let E be a real Banach space, and let C be a nonempty closed convex subset E. In 2007, Marino and Xu 2 showed that the Mann iterative sequence converges weakly to a fixed point of λ-strict pseudocontractions in Hilbert spaces.

Results

Conclusion