Zs-contractive mappings and weak compatibility in fuzzy metric space

Abstract

The aim of this paper is to introduce Zs-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]), pscontraction (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.

Keywords

• fuzzy metric space
• t-norm
• m-cauchy sequence
• common fixed points
• zs-contraction
• weak compatibility