Common Fixed Point Theorem in Fuzzy Metric Space Using Control Function

Kumar, Amit; Vats, Ramesh Kumar

doi:10.4134/ckms.2013.28.3.517

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Definition 15 the 5-tuple (X M N * ) Is Said To Be An1

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Cited by 2 publications

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“…The involvement of altering distance sometimes requires special techniques as the triangular inequality does not remain directly applicable. Using the control function considerable work have been done (see [10] and by Θ we denote the set of all functions α :…”

Section: Definition 15 the 5-tuple (X M N * ) Is Said To Be Anmentioning

confidence: 99%

Fixed Point Theorems for Weak Contraction in Intuitionistic Fuzzy Metric Space

Vats¹,

Grewal²

2016

Honam Mathematical Journal

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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 (ψ, α, β)-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.

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Section: Definition 15 the 5-tuple (X M N * ) Is Said To Be Anmentioning

confidence: 99%