Best Proximity Pairs for Upper Semicontinuous Set-Valued Maps in Hyperconvex Metric Spaces
نویسندگان
چکیده
1 Department of Mathematics, Faculty of Basic Sciences, University of Shahrekord, Shahrekord 88186-34141, Iran 2 Department of Mathematics, School of Science, Razi University, Kermanshah 67149, Iran 3 Department of Mathematics, College of Arts, Social Sciences and Celtic Studies, National University of Ireland, Galway, Ireland 4 Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne, FL 32901, USA
منابع مشابه
Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces
The best approximation problem in a hyperconvex metric space consists of finding conditions for given set-valued mappings F andG and a setX such that there is a point x0 ∈ X satisfying d G x0 , F x0 ≤ d x, F x0 for x ∈ X. When G I, the identity mapping, and when the set X is compact, best approximation theorems for mappings in hyperconvex metric spaces are given for the single-valued case in 1–...
متن کاملBest proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$
متن کاملBest Proximity Points Results for Cone Generalized Semi-Cyclic φ-Contraction Maps
In this paper, we introduce a cone generalized semi-cyclicφ−contraction maps and prove best proximity points theorems for such mapsin cone metric spaces. Also, we study existence and convergence results ofbest proximity points of such maps in normal cone metric spaces. Our resultsgeneralize some results on the topic.
متن کاملContinuous Selections and Approximations in Α-convex Metric Spaces
In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.
متن کاملResults on the Existence and Convergence of Best Proximity Points
We first consider a cyclic φ-contraction map on a reflexive Banach space X and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic φ-contraction maps in reflexive Banach spaces in one of their works 2009 . In the second part of the paper, we will discuss the existence of best proximity points in the framework of more gene...
متن کامل