A Common Fixed Point Theorem in Fuzzy Metric Spaces Using Sb- Function

INTRODUCTION The concept of fuzzy sets introduced by Zadeh [19], was the foundation of fuzzy metric space. Fuzzy metric spaces have been introduced by Kramosil and Michalek [8] and George and Veeramani [3] modified the notion of fuzzy metric spaces with the help of continuous tnorm. Recently many authors such as [4], [7], [14] and [15] have proved fixed point theorems involving fuzzy sets. Bouhajera and Godet-Thobie [1] proved common fixed point theorems by using the concept of sub compatible maps. Later Singh, Jain and Wani [17] introduced the concept of sub compatibility and sub sequential continuity which are weaker than occasional weak compatibility in fuzzy metric spaces. Recently Sastry, Srinivasa Rao and Bhaskar [11] have introduced the notion of SB-function and used them as control functions to find a common fixed point for four self maps. In this paper we use SB-function as control functions to find common fixed point for four self maps which are sub compatible and sub sequentially continuous in pairs. We also provide an example of a pair of maps which is sub compatible and sub sequentially continuous but not occasional weak continuous. Also we obtain the results of Singh, Jain and Wani. [17] and Sastry, Srinivasa Rao and Bhaskar [11] as corollaries.