$Z_s$-Contractive Mappings and Weak Compatibility in Fuzzy Metric Space

Shobha Jain, Shishir Jain

The aim of this paper is to introduce $Z_s$-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges and unifies the existing fuzzy contractions (by Gregori and Sapena 4]), $\psi$-contraction (by Mihet [8]), $Z$-contractions (by Shukla [15]) and Tirado contraction [16]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [15] through weak compatibility. The article includes an example, which shows the validity of our results.