Implicit Iterations of Two Finite Families for Nonexpansive Mappings in Banach Spaces.

The purpose of this paper is to study the weak and strong convergence of an implicit iteration process to a common fixed point for two finite families of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Xu and Ori, Numer. Funct. Anal. Optim. 2001; 22:767-773, Zhou and Chang, Numer. Fund. Anal. Optim. 2002; 23:911-921, Chidume and Shahzad, Nonlinear. Anal. 2005; 62: 1149-1156. [ABSTRACT FROM AUTHOR]