Weak and Strong Convergence of an Explicit Iteration Process for a Total Asymptotically Quasi-I-Nonexpansive Mapping in Banach Spaces

Abstract

In this paper, we introduce a new class of Lipschitzian maps and prove the weak and strong convergence of the explicit iterative process to a common fixed point of a total asymptotically quasi-I-nonexpansive mapping T and a total asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.