Abstract—The object of this paper is to introduce the concept of a pair of semi-compatible self-maps and sub compatibility in fuzzy metric spaces In this paper, we also introduce the notion of M-maps with respect to a single map and a pair of maps in fuzzy metric spaces and obtain common fixed point theorems for two pairs of sub compatible and semi compatible maps satisfying implicit relations.

Index Terms—Common fixed point theorem, fuzzy metric space, semi-compatibility, sub-compatibility, set valued M-maps.

Sonal Dani is with the Department of Applied Mathematics Chhatrapati Shivaji Institute of Technology, Durg(C.G) India (e-mail: sonaldani18@gmail.com).
Sanjay Sharma is with the Department of Applied Mathematics Bhilai Institute of Technology, Durg(C.G) India (e-mail: ssharma_bit@yahoo.co.in).

Cite:Sonal Dani and Sanjay Sharma, "Common Fixed Point Theorem for Semi-Compatible and Sub Compatible Maps in Fuzzy Metric Space," International Journal of Applied Physics and Mathematics vol. 3, no. 3, pp. 188-190, 2013.