Abstract and Applied Analysis

Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets

Wiesława Kaczor

Full-text: Open access

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 {Ci:1in} of X, and each Ci 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

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050426053

Digital Object Identifier
doi:10.1155/S1085337503205054

Mathematical Reviews number (MathSciNet)
MR1960139

Zentralblatt MATH identifier
1032.47030

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H09
Secondary: 47H20

Citation

Kaczor, Wiesława. Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets. Abstr. Appl. Anal. 2003 (2003), no. 2, 83--91. doi:10.1155/S1085337503205054. https://projecteuclid.org/euclid.aaa/1050426053


Export citation