Abstract
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.
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