Bernstein–Doetsch Type Theorems with Tabor Type Error Terms for 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...

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

Fixed Point Theorems for Set-Valued Contraction Type Maps in Metric Spaces

Best Proximity Pairs Theorems for Continuous Set-Valued Maps

Continuity Properties of Convex-type Set-valued Maps

K–convex, K–midconvex and (K,λ)–convex set–valued maps are considered. Several conditions implying the continuity of such maps are collected.