Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces.

The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping T and a finite family of nonexpansive mappings {Ti}_i=1^N, respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others. [ABSTRACT FROM AUTHOR]