The first common fixed point theorem for commutative set-valued mappings

2017/07/18 by Mohamadi, Issa
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1707.06098

Abstract

We establish the first common fixed point theorem for commutative set-valued mappings. This may help to generalize common fixed point theorems in single-valued setting to those in set-valued. We also prove the existence of a fixed point in a continuously expanding set under a none convex upper semicontinuous set-valued mapping; as a result we answer positivly to a question of Lau and Yao.

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