APPROXIMATING COMMON FIXED POINT OF UNIFORMLY QUASI-LIPSCHITZIAN MAPPINGS      BY -STEP ITERATIVE SCHEME WITH ERRORS

Jian-Zhong Xiao (P. R. China), Xuan Huang (P. R. China) and Jing Sun (P. R. China)

Received October 1, 2007

Abstract

In this paper a -step iterative scheme is studied with errors involving k uniformly quasi-Lipschitzian mappings and 1 asymptotically j-hemicontractive mapping in Banach spaces. Some new convergence theorems are established for the iterative scheme to approximate a common fixed point of these  mappings. The results presented in this paper extend, unify and improve several recent important results obtained by Zeng [14], Chang [3], Xiao and Zhu [11], and others.

Keywords and phrases: asymptotically j-hemicontractive mapping, uniformly quasi-Lipschitzian mappings, -step iterative scheme, common fixed point, Banach space.