New Simple Approximation Algorithm of Fixed Point for Nonexpansive Mappings
非扩张映像不动点新的简单逼近算法

The purpose of this article is to establish new simple approximative algorithms of fixed point for nonexpansive mappings and to prove new fixed point theorems for nonexpansive mappings in the reflexive Banach spaces. The approximate algorithms presented in this article are simpler than Mann, Ishikawa and Halpern iterative algorithms. The weak and strong convergence theorems are proved respectively. The new fixed point theorems presented here improve and extend the related results of Goebel-Kirk, Kim-Xu and others in some respects.