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2020 Function and colorful extensions of the KKM theorem
Władysław Kulpa, Andrzej Szymański, Marian Turzański
Topol. Methods Nonlinear Anal. 56(1): 313-324 (2020). DOI: 10.12775/TMNA.2020.015

Abstract

We deal with an aggregate version of the KKM theorem. Given $n$ KKM families of special type on an $( n-1)$-dimensional simplex, we show that it is possible to choose a single element from every KKM family to get a KKM family on that simplex. We also introduce and study function KKM families as surrogates of KKM families on simplexes. We show a function version of the KKM theorem. The Coincidence Theorem is our main result, Brouwer's fixed is a special cases of that theorem.

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Władysław Kulpa. Andrzej Szymański. Marian Turzański. "Function and colorful extensions of the KKM theorem." Topol. Methods Nonlinear Anal. 56 (1) 313 - 324, 2020. https://doi.org/10.12775/TMNA.2020.015

Information

Published: 2020
First available in Project Euclid: 16 October 2020

MathSciNet: MR4175081
Digital Object Identifier: 10.12775/TMNA.2020.015

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 1 • 2020
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