Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 457935, 10 pages
doi:10.1155/2010/457935
Research Article

Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces

A. Abkar and M. Eslamian

Department of Mathematics, Imam Khomeini International University, P.O.Box 288, Qazvin 34149, Iran

Received 1 March 2010; Accepted 17 June 2010

Academic Editor: Tomás Dominguez Benavides

Copyright © 2010 A. Abkar and M. Eslamian. 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.

Abstract

In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006). In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly L(τ) spaces; our result generalizes a recent result of Domínguez-Benavides et al. (2009).