Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 819269, 14 pages
doi:10.1155/2010/819269
Research Article

Some Common Fixed Point Theorems in Menger PM Spaces

M. Imdad,1 M. Tanveer,2 and M. Hasan3

1Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
2School of Computer & Systems Sciences, Jawaharlal Nehru University, New Delhi 110 067, India
3Department of Applied Mathematics, Aligarh Muslim University, Aligarh 202 002, India

Received 11 May 2010; Accepted 11 August 2010

Academic Editor: Tomonari Suzuki

Copyright © 2010 M. Imdad et al. 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

Employing the common property (E.A), we prove some common fixed point theorems for weakly compatible mappings via an implicit relation in Menger PM spaces. Some results on similar lines satisfying quasicontraction condition as well as ψ-type contraction condition are also proved in Menger PM spaces. Our results substantially improve the corresponding theorems contained in (Branciari, (2002); Rhoades, (2003); Vijayaraju et al., (2005)) and also some others in Menger as well as metric spaces. Some related results are also derived besides furnishing illustrative examples.