Weak and Strong Convergence of an Implicit Iteration Process for Two Families of Asymptotically Nonexpansive Mappings

Sun Young Cho, Shin Min Kang, Xiaolong Qin

Abstract

In this paper, we consider an implicit iterative process for two finite families of asymptotically nonexpansive mappings in the framework of a real uniformly convex Banach space. The results presented in this paper mainly improve and extend the recent ones announced in [S. S. Chang, K. K. Tan, H. W. J. Lee and C. K. Chan, On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 313 (2006), 273–283] and [S. H. Khan, I. Yildirim and M. Ozdemir, Convergence of an implicit algorithm for two families of nonexpansive mappings, Comput. Math. Appl., 59 (2010), 3084–3091].