Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 297360, 14 pages doi: Research Article Impact of Common Property (.) on Fixed Point Theorems in Fuzzy Metric Spaces D. Gopal,1 M. Imdad,2 and C. Vetro3 1 Department of Mathematics and Humanities, National Institute of Technology, Surat, Gujarat 395007, India 2 Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India 3 Dipartimento di Matematica e Informatica, Universit` degli Studi di Palermo, Via Archirafi 34, a 90123 Palermo, Italy Correspondence should be addressed to D. Gopal, Received 7 November 2010; Accepted 9 March 2011 Academic Editor: Jerzy Jezierski Copyright q 2011 D | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 297360 14 pages doi 2011 297360 Research Article Impact of Common Property . on Fixed Point Theorems in Fuzzy Metric Spaces D. Gopal 1 M. Imdad 2 and C. Vetro3 1 Department of Mathematics and Humanities National Institute of Technology Surat Gujarat 395007 India 2 Department of Mathematics Aligarh Muslim University Aligarh 202002 India 3 Dipartimento di Matematica e Informatica Universita degli Studi di Palermo Via Archirafi 34 90123 Palermo Italy Correspondence should be addressed to D. Gopal Received 7 November 2010 Accepted 9 March 2011 Academic Editor Jerzy Jezierski Copyright 2011 D. Gopal 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. We observe that the notion of common property . relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence a multitude of recent fixed point theorems of the existing literature are sharpened and enriched. 1. Introduction and Preliminaries The evolution of fuzzy mathematics solely rests on the notion of fuzzy sets which was introduced by Zadeh 1 in 1965 with a view to represent the vagueness in everyday life. In mathematical programming the problems are often expressed as optimizing some goal functions equipped with specific constraints suggested by some concrete practical situations. There exist many real-life problems that consider multiple objectives and generally it is very difficult to get a feasible solution that brings us to the optimum of all the objective functions. Thus a feasible method of resolving such problems is the use of fuzzy sets 2 . In fact the richness of applications has engineered the all round development
