Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 172532 | https://doi.org/10.1155/S1085337503203080

T. Domínguez Benavides, P. Lorenzo Ramírez, "Fixed-point theorems for multivalued non-expansive mappings without uniform convexity", Abstract and Applied Analysis, vol. 2003, Article ID 172532, 12 pages, 2003. https://doi.org/10.1155/S1085337503203080

Fixed-point theorems for multivalued non-expansive mappings without uniform convexity

Received13 Sep 2001

Abstract

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(C) the family of all compact convex subsets of C, and T a nonexpansive mapping from C into KC(C). We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is a 1-χ-contractive mapping.

Copyright © 2003 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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