## Abstract and Applied Analysis

### Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets

Wiesława Kaczor

#### Abstract

It is shown that if $X$ is a Banach space and $C$ is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets $\{C_i: 1\leq i\leq n\}$ of $X$, and each $C_i$ has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of $C$ has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach spaces with Opial's property.

#### Article information

Source
Abstr. Appl. Anal., Volume 2003, Number 2 (2003), 83-91.

Dates
First available in Project Euclid: 15 April 2003

https://projecteuclid.org/euclid.aaa/1050426053

Digital Object Identifier
doi:10.1155/S1085337503205054

Mathematical Reviews number (MathSciNet)
MR1960139

Zentralblatt MATH identifier
1032.47030

Subjects