Won Kyu Kim
Abstract
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In this paper, we first introduce an R-E-KKM map in the E-convex settings, and next we prove an R-E-KKM theorem which generalizes the KKM theorem and the best proximity theorem simultaneously. As applications, a best proximity theorem and a fixed point theorem in E-convex sets are given.
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In this paper, we first introduce an R-E-KKM map in the E-convex settings, and next we prove an R-E-KKM theorem which generalizes the KKM theorem and the best proximity theorem simultaneously. As applications, a best proximity theorem and a fixed point theorem in E-convex sets are given.
Key concepts: Fixed-point theorem, Danskin's theorem, Brouwer fixed-point theorem, Regular polygon, Mathematics, Mean value theorem (divided differences), Kakutani fixed-point theorem, Picard–Lindelöf theorem