Common fixed points of compatible maps in fuzzy metric spaces

Singh, Bijendra; Chauhan, M. S.

doi:10.1016/s0165-0114(98)00099-2

Cited by 79 publications

(53 citation statements)

References 4 publications

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“…This research extended and generalized the results of Singh and Chauhan ( [14], 2000). We give some definitions and properties of intuitionistic fuzzy metric space.…”

Section: Isupporting

confidence: 84%

Semi-Compatible Maps On Intuitionistic Fuzzy Metric Space

Dwivedi¹

2013

IOSR-JM

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Abstract:In this paper, we prove common fixed point theorem for semi-compatible mappings on intuitionistic fuzzy metric space with different some conditions of Park and Kim ([10], 2008). This research extended and generalized the results of Singh and Chauhan ([14], 2000).The concept of fuzzy set was developed extensively by many authors and used in various fields. Several authors have defined fuzzy metric space Kramosil and Michalek(([5],1975) etc.) with various methods to use this concept in analysis. Jungck (([3],1986), ([4],1988)) researched the more generalized concept compatibility than commutativity and weak commutativity in metric space and proved common fixed point theorems, and Singh and Chauhan ([14],2000) introduced the concept of compatibility in fuzzy metric space and studied common fixed point theorems for four compatible mappings. Recently, Park et. al. ([7], 2006) defined the upgraded intuitionistic fuzzy metric space and Park et.al. (([8], 2008), ([9], 1999), ([11], 2007), ([12], 2005)) studied several theories in this space. Also, Park and Kim ([10], 2008) proved common fixed point theorem for self maps in intuitionistic fuzzy metric space.

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“…This research extended and generalized the results of Singh and Chauhan ( [14], 2000). We give some definitions and properties of intuitionistic fuzzy metric space.…”

Section: Isupporting

confidence: 84%

Semi-Compatible Maps On Intuitionistic Fuzzy Metric Space

Dwivedi¹

2013

IOSR-JM

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“…Singh and Chauhan [7], Vasuki [8] and Wang et al [9] studied the common fixed points in fuzzy metric spaces. De la Sen et al [10,11] studied the so-called fuzzy best proximity points and fuzzy best proximity coincidence points.…”

Section: Introductionmentioning

confidence: 99%

Common Coincidence Points and Common Fixed Points in Fuzzy Semi-Metric Spaces

2018

Mathematics

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Abstract:We propose the so-called fuzzy semi-metric space in which the symmetric condition is not assumed to be satisfied. In this case, there are four kinds of triangle inequalities that should be considered. The purpose of this paper is to study the common coincidence points and common fixed points in the newly proposed fuzzy semi-metric spaces endowed with the so-called -triangle inequality. The other three different kinds of triangle inequalities will be the future research, since they cannot be similarly investigated as the case of -triangle inequality.

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“…Recently, Grabiec [10] has proved fixed point results for Fuzzy metric space. In the sequel, Singh and Chauhan [16] introduced the concept of compatible mappings in Fuzzy metric space and proved the common fixed point theorem. Jungck et al [17] introduced the concept of compatible maps of type (A) in metric space and proved fixed point theorems.…”

Section: Introductionmentioning

confidence: 99%

Fixed Points for Subsequential Continuous Mappings in Fuzzy Metric Space

Jain¹,

Badshah²,

Gupta³

et al. 2014

IJAPM

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Abstract:In the present paper, first we introduce the notion of subsequential continuous mappings in the framework of fuzzy metric space and show that this concept is more general than continuous mappings as well as reciprocal continuous mappings. Also, we cited an example in support of this. Secondly, we introduce the concept of occasionally weakly compatible mappings which is more general than weakly compatible mappings in fixed point theory. At the end, we prove an interesting common fixed point theorem in fuzzy metric space for four self mappings by employing the notion of subsequential continuity, occasionally weakly compatible mappings and semi-compatible mappings.2000 Mathematics Subject Classification. 54H25, 47H10.

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Common fixed points of compatible maps in fuzzy metric spaces

Cited by 79 publications

References 4 publications

Semi-Compatible Maps On Intuitionistic Fuzzy Metric Space

Semi-Compatible Maps On Intuitionistic Fuzzy Metric Space

Common Coincidence Points and Common Fixed Points in Fuzzy Semi-Metric Spaces

Fixed Points for Subsequential Continuous Mappings in Fuzzy Metric Space

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