Abstract convexity in KKM theorems via set-valued maps

Abstract

Different aspects of the KKM Lemma besides its vast applications in nonlinear analysis have been investigated over the years. Some researchers tried to present the KKM results such as generalized L-KKM type theorems in the absence of usual convexity. Here, first we present a counterexample to show that the main results in some generalized KKM type theorems and their consequences are not valid. Afterward, the uniform mapconvex space is introduced and a nonempty intersection result in this space is proved. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.