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The first common fixed point theorem for commutative set-valued mappings (1707.06098v2)
Published 18 Jul 2017 in math.FA and math.CA
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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