Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces

Abstract

We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping $\left\{T_i\right\}$ in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each $T_i$. Some strong convergence theorems of the proposed method are also obtained for the following cases: all $T_i$ are continuous and one of $T_i$ is hemicompact, and the domain $K$ is compact.