Strong Convergence For Finding Fixed Point Of Multi-Valued Mapping

It is known that the Mann iteration is for approximating fixed points of nonexpans-ive single-valued mappings. However, in general the Mann iteration process has only weak convergence. In recent years, Sastry, Babu and Panyanak introduced the Mann and Ishikawa iteration scheme for non-expansive multi-valued mapping and obtained the strong convergen-ce theorems. In this paper, we introduce a new iterative method for quasi-nonexpansive multi-valued maps in Banach spaces, and obtain the strong convergence theorems.