Best Proximity Pairs Theorems for Continuous Set-Valued Maps

Best Proximity Pairs Theorems for Continuous Set-Valued Maps

Best 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 $$d(G(x_0),F(x_0))=d(A,B).$$

best 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 $$d(g(x_0),f(x_0))=d(a,b).$$

Best Proximity Pairs for Upper Semicontinuous Set-Valued Maps in Hyperconvex Metric Spaces

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 I...

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–...