• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.159-180
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• 2013

We establish a common fixed point theorem for mappings under ${\phi}$-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.2
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• pp.108-112
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• 2011

Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in intuitionistic fuzzy metric space.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.391-399
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• 2007

The purpose of this paper is to obtain some common fixed point theorems for multivalued mappings in intuitionistic fuzzy metric space. We extend some earlier results.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.19-30
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• 2009

In this paper, we prove some common fixed point theorems for six maps satisfying compatible maps of type(${\alpha}$) on intuitionistic fuzzy metric spaces in sense of Park et al.[7]. Our research are generalization and extension for the results of [1], [2], [3] and [13].

• Honam Mathematical Journal
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• v.38 no.2
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• pp.337-357
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• 2016

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.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.11-23
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• 2013

In this paper, we obtain a common fixed point theorem for multivalued mappings in a complete Menger $\mathcal{L}$-fuzzy metric space. $\mathcal{L}$-fuzzy metric space is a generalization of fuzzy metric spaces and intuitionistic fuzzy metric spaces. We extend and generalize the results of Kubiaczyk and Sharma [24], Sharma, Kutukcu and Rathore [34].

• Honam Mathematical Journal
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• v.34 no.1
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• pp.77-84
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• 2012

In this paper, we define the weakly commuting mapping and prove the fixed point theorem for weakly commuting mappings under some conditions on intuitionistic fuzzy metric spaces.