Fixed point theorems of mean nonexpansive set-valued mappings in Banach spaces

摘要

We introduce the concept of a mean nonexpansive set-valued mapping in Banach spaces, and extend Nadler's fixed point theorem and Lim's fixed point theorem to the case of mean nonexpansive set-valued mappings. Furthermore, using the characteristic of convexity, Opial property, and (DL)-condition, necessary and sufficient conditions for mean nonexpansive set-valued mappings which have the stationary points in Banach spaces are obtained.