Fixed Points Theorems for $n$-Valued Multifunctions

Abstract: We first show that if $Y$ is a nonempty AR space and $F\colon Y \rightarrow Y$ is a compact $n$-valued multifunction, then $F$ has at least $n$ fixed point. We also prove that if $C$ is a nonempty closed convex subset of a topological vector space $E$ and $F \colon C \rightarrow C$ is a continuous $\Phi$-condensing $n$-valued multifunction, then $F$ has at least $n$ fixed points.

Keywords: AR spaces, $n$-valued multifunction, convex set, fixed point, $\Phi$-condensing multifunction

Classification (MSC2000): 46A55; 52A07, 54H25

Full text of the article:

• Compressed PostScript file (136 kilobytes)
• PDF file (168 kilobytes)