# FIXED POINT THEOREMS FOR WEAK CONTRACTION IN INTUITIONISTIC FUZZY METRIC SPACE

• Vats, Ramesh Kumar (Department of Mathematics, National Institute of Technology) ;
• Grewal, Manju (Department of Mathematics, National Institute of Technology)
• Accepted : 2016.04.11
• Published : 2016.06.25
• 98 8

#### Abstract

The notion of weak contraction in intuitionistic fuzzy metric space is well known and its study is well entrenched in the literature. This paper introduces the notion of (${\psi},{\alpha},{\beta}$)-weak contraction in intuitionistic fuzzy metric space. In this contrast, we prove certain coincidence point results in partially ordered intuitionistic fuzzy metric spaces for functions which satisfy a certain inequality involving three control functions. In the course of investigation, we found that by imposing some additional conditions on the mappings, coincidence point turns out to be a fixed point. Moreover, we establish a theorem as an application of our results.

#### Keywords

common fixed point;fuzzy metric space;control function;weak contraction

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