Borsuk’s antipodal fixed points theorems for compact or condensing set-valued maps

Structure of the Fixed Point of Condensing Set-Valued Maps

In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.

Fixed Point Theorems For Set-Valued Maps

Preface In this thesis we provide an introduction to fixed point theory for set-valued maps. It is not our goal in the present work to give an outline of the status quo of fixed point theory with all its newest achievements, but rather to give a thorough overview of the basic results in this discipline. It then should be possible for the reader to better and easier understand the newest develop...

Fixed Points of Compact Kakutani Maps with Antipodal Boundary Conditions

We prove a fixed-point result for compact upper semicontinuous compact-convex-valued multifunctions satisfying antipodal boundary conditions on bounded symmetric subsets of a normed space. Two types or antipodal conditions are considered.

Fixed Point Theorems for Set-valued Mappings

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