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

We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping {T-i} 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.