International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2002 / Article

Open Access

Volume 31 |Article ID 146534 | 7 pages | https://doi.org/10.1155/S0161171202107113

Fixed point theorems for nonexpansive mappings on nonconvex sets in UCED Banach spaces

Received25 Jul 2001
Revised10 Jan 2002

Abstract

It is shown that every asymptotically regular or λ-firmly nonexpansive mapping T:CC has a fixed point whenever C is a finite union of nonempty weakly compact convex subsets of a Banach space X which is uniformly convex in every direction. Furthermore, if {Ti}iI is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of Ti, i I, have a nonempty intersection, then Ti, iI, have a common fixed point in C.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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