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FIXED POINT THEOREMS FOR WEAK CONTRACTION IN INTUITIONISTIC FUZZY METRIC SPACE
Vats, Ramesh Kumar,Grewal, Manju The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.2
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.
Fixed point theorems for weak contraction in Intuitionistic fuzzy metric space
Ramesh Kumar Vats,Ramesh Kumar Vats 호남수학회 2016 호남수학학술지 Vol.38 No.2
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.
COMMON FIXED POINT THEOREM IN FUZZY METRIC SPACE USING CONTROL FUNCTION
Kumar, Amit,Vats, Ramesh Kumar Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.3
We give a fixed point theorem for complete fuzzy metric space which generalizes fuzzy Banach contraction theorems established by V. Gregori and A. Spena [Fuzzy Sets and Systems 125 (2002), 245-252] using notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9] in metric spaces.