A new one-step implicit iterative process for common fixed points of two asymptotically nonexpansive mappings in Banach spaces

Abstract

The purpose of this paper is to introduce an implicit iteration process for approximating common fixed points of two finite families of asymptotically nonexpansive mappings { T j } j = 1 N and { S j } j = 1 N in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding results of Chang et al. (2006) [3], Chidume and Shahzad (2005) [4], Guo and Cho (2008) [8], Qin et al. [10], Sun (2003) [13], Xu and Ori (2001) [14], Zhao et al. (2008) [15], Zhao and Wang (2009) [16], Zhou and Chang (2002) [17], Zhou et al. (2006) [18].