A fixed point theorem of Markov-Kakutani type for a commuting family of convex multivalued maps


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	A fixed point theorem of Markov-Kakutani type for a commuting family of convex multivalued maps


	Fixed Point Theory, Volume 18, No. 1, 2017, 155-166, March 1st, 2017 DOI: 10.24193/fpt-ro.2017.1.13 Authors: Xiongping Dai Abstract: Let Γ be a commuting family of upper semicontinuous convex multivalued maps of K into itself with nonempty closed values, where K is a nonempty compact convex subset of a locally convex Hausdorff topological vector space E. We then show that the Markov-Kakutani fixed-point theorem holds; that is, there exists at least one point x ∈ K such that x ∈ u(x) for all u in Γ. Key Words and Phrases: fixed-point theorem, multimaps, invariant measure of multimaps, locally convex Hausdorff topological space. 2010 Mathematics Subject Classification: 47H10, 54H25, 54C60. Published on-line: March 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents