Common Fixed Points of a Finite Family of Nonself Generalized Asymptotically Quasi-Nonexpansive Mappings

Abstract

Suppose that $C$ is a nonempty subset of a real Banach space $X$. In this article, we construct two types of iterative schemes with errors for a finite family $\{T_i\}_{i=1}^k$ of nonself generalized asymptotically quasi-nonexpansive mappings of $C$ into $X$. Furthermore, not only a necessary and sufficient condition for $\{x_n\}$ generated by each of those iterations to converge to a common fixed point of $\{T_i\}_{i=1}^k$ is obtained, but also the weak and strong convergence theorems of $\{x_n\}$ in uniformly convex Banach spaces are established as well.