Common Fixed Point Theorems for Compatible Maps in Generalized Fuzzy Metric Spaces
M. Jeyaraman *
PG and Research Department of Mathematics, Raja Doraisingam Govt. Arts College, Sivaganga, Affiliated to Alagappa University, Karaikudi, India.
S. Sowndrarajan
PG and Research Department of Mathematics, Raja Doraisingam Govt. Arts College, Sivaganga, Affiliated to Alagappa University, Karaikudi, India.
A. Ramachandran
Department of Mathematics, Suvarna Karnataka Institute of Studies and Research Center, Tumkur, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we consider generalized fuzzy metric spaces and provide existence and uniqueness fixed point results. First, we use compatible maps of type (β) to prove fixed point results, then we introduce weakly compatible maps to approximate common fixed point results by using an implicit relation.
Keywords: Fixed point theorem, generalized fuzzy metric space, implicit relations