REMARKS ON THE KKM PROPERTY FOR OPEN-VALUED MULTIMAPS ON GENERALIZED CONVEX SPACES

Title & Authors
REMARKS ON THE KKM PROPERTY FOR OPEN-VALUED MULTIMAPS ON GENERALIZED CONVEX SPACES
KIM HOONJOO; PARK SEHIE;

Abstract
Let (X, D; $\small{{\Gamma}}$) be a G-convex space and Y a Hausdorff space. Then $\small{U^K_C}$(X, Y) $\small{{\subset}}$ KD(X, Y), where $\small{U^K_C}$ is an admissible class (dup to Park) and KD denotes the class of multimaps having the KKM property for open-valued multimaps. This new result is used to obtain a KKM type theorem, matching theorems, a fixed point theorem, and a coincidence theorem.
Keywords
KKM principle;generalized convex (G-convex) spaces;multimaps having the KKM property;multimaps having the KKM property;
Language
English
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