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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2617-2629

Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation

1School of Studies in Mathematics, Vikram University, University Road Ujjain, Madhya Pradesh 456010, India
2Shri Vaishnav Institute of Technology and Science, Indore, Madhya Pradesh 453331, India

Received 27 January 2005; Revised 29 May 2005

Copyright © 2005 Bijendra Singh and Shishir Jain. 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.


The concept of semicompatibility has been introduced in fuzzy metric space and it has been applied to prove results on existence of unique common fixed point of four self-maps satisfying an implicit relation. Recently, Popa (2002) has employed a similar but not the same implicit relation to obtain a fixed point theorem for d-complete topological spaces. All the results of this paper are new.