Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Some Common Fixed Point Theorems in Menger PM Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 819269 14 pages doi 2010 819269 Research Article Some Common Fixed Point Theorems in Menger PM Spaces M. Imdad 1 M. Tanveer 2 and M. Hasan3 1 Department of Mathematics Aligarh Muslim University Aligarh 202 002 India 2 School of Computer Systems Sciences Jawaharlal Nehru University New Delhi 110 067 India 3 Department of Applied Mathematics Aligarh Muslim University Aligarh 202 002 India Correspondence should be addressed to M. Tanveer tanveer_gouri@ 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. Employing the common property 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 y-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. 1. Introduction and Preliminaries Sometimes it is found appropriate to assign the average of several measurements as a measure to ascertain the distance between two points. Inspired from this line of thinking Menger 1 2 introduced the notion of Probabilistic Metric spaces in short PM spaces as a generalization of metric spaces. In fact he replaced the distance function d R X R R with a distribution function Fp q R 0 1 wherein for any number x the value Fpq x describes the probability that the distance between p and q is less than x. In fact the study
