The purpose of this paper is to study the weak and strong convergence of two implicit iteration processes to a common fixed point for two nonexpansive mappings and two finite families of nonexpansive mappings, respectively, in Banach spaces. The result presented in this paper improves and extends the corresponding results of Xu and Ori [8], Zhao et al. [9], Chidume and Shahzad [2], and others.

implicit iteration process, Strong and weak convergence theorems, common fixed point.