Coincidence indices for set-valued compact mapping pairs

Generalized coincidence theory for set-valued maps

This paper presents a coincidence theory for general classes of maps based on the notion of a Φ-essential map (we will also discuss Φ-epi maps). c ©2017 All rights reserved.

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

The Coincidence Problem for Compositions of Set-valued Maps

If A is compact, then A and B have a coincidence, that is, there exists (z0, Vo) € X x Y with y0 G A(x0) D B(x0). [Recall that a nonempty compact space is acyclic if all its reduced Cech homology groups over Q vanish.] The proof of Theorem 0 relies on a Lefschetz-type fixed point theorem of Gorniewicz and Granas [14] which is itself based on sophisticated homological machinery. One of our conce...

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