Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 692401, 14 pages
doi:10.1155/2010/692401
Research Article

On Uniformly Generalized Lipschitzian Mappings

M. Imdad1 and Ahmed H. Soliman2

1Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt

Received 30 November 2009; Revised 23 February 2010; Accepted 11 April 2010

Academic Editor: Anthony To Ming Lau

Copyright © 2010 M. Imdad and Ahmed H. Soliman. 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

We consider another class of generalized Lipschitzian type mappings and utilize the same to prove fixed point theorems for asymptotically regular and uniformly generalized Lipschitzian one-parameter semigroups of self-mappings defined on bounded metric spaces equipped with uniform normal structure which yield corresponding results in respect of semigroup of iterates of a self-mapping as corollaries. Our results also generalize some relevant results due to the work of Lim and Xu (1995), Yao and Zeng (2007), and Soliman (2009).