Common Fixed Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces

Sintunavarat, Wutiphol; Kumam, Poom

doi:10.1155/2011/637958

Cited by 170 publications

(145 citation statements)

References 40 publications

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“…Although the property (E.A) is a generalization of the concepts of non-compatible as well as non-vacuous compatible pairs, yet such results do require either completeness of the whole space or any one of the range subspaces or continuity conditions on the involved maps. But, quite contrary to this, the new notion of (CLR S )-property recently given by Sintunavarat and Kumam [8] does not impose such conditions. The importance of (CLR S )-property ensures that one does not require the completeness of the whole space or closedness of range subspaces.…”

Section: Introduction With Preliminariesmentioning

confidence: 90%

Common Fixed Point Theorems for Mappings under (CLRS)-Property in Partial Metric Spaces

Rao¹,

Imdad²,

Parvathi³

2016

Demonstratio Mathematica

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Abstract. In this paper, we introduce the concept of (CLRS)-property for mappings F : XˆX Ñ X and S : X Ñ X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems. Introduction with preliminariesIn 2002, Aamri and El-Moutawakil [1] introduced the idea of the property (E.A) for a pair of self mappings defined on a metric space, which contains the classes of non-vacuously compatible as well as non-compatible mappings in metric spaces as proper subclasses and utilized the same to prove common fixed point theorems under strict contractive condition. Although the property (E.A) is a generalization of the concepts of non-compatible as well as non-vacuous compatible pairs, yet such results do require either completeness of the whole space or any one of the range subspaces or continuity conditions on the involved maps. But, quite contrary to this, the new notion of (CLR S )-property recently given by Sintunavarat and Kumam [8] does not impose such conditions. The importance of (CLR S )-property ensures that one does not require the completeness of the whole space or closedness of range subspaces.Nazir and Abbas [6] introduced the property (E.A) for a pair of self maps in partial metric spaces. In this paper, we introduce the concept of (CLR S )-property for the maps F : XˆX Ñ X and S : X Ñ X in a partial metric space and utilize the same to prove two unique common fixed point theorems for four mappings in partial metric spaces. As usual, let us denote 2010 Mathematics Subject Classification: 54H25, 47H10.

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Section: Introduction With Preliminariesmentioning

confidence: 90%

Common Fixed Point Theorems for Mappings under (CLRS)-Property in Partial Metric Spaces

Rao¹,

Imdad²,

Parvathi³

2016

Demonstratio Mathematica

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“…All authors read and approved the final manuscript. 1 Department of Mathematics, University of Jaén, Campus Las Lagunillas, s/n, Jaén, 23071, Spain.…”

Section: Competing Interestsmentioning

confidence: 99%

Irremissible stimulate on ‘Unified fixed point theorems in fuzzy metric spaces via common limit range property’

Hierro

Karapınar

2014

J Inequal Appl

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One of the goals of this short note is to alert researchers as regards some mistakes that appeared in a recent paper (Chauhan, Khan and Kumar in J. Inequal. Appl. 2013:182, 2013). This entails main proofs based on a false result, which invalidates all statements. We also give a complete revision of the antecedents of this work in order to find the main reasons of the mistakes. Finally, the main aim of this note is to propose a correct, more general version of the main theorems in the paper mentioned.

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“…In 2011, using the concept of compatible maps of type (A) and type (), Singh et al [19], [20] proved fixed point theorems in a fuzzy metric space. Recently, Sintunavarat and Kumam [21] defined the notion of (CLRg) property in fuzzy metric spaces and improved the results of Mihet [22] without any requirement of the closedness of the subspace. Recently in 2012, Jain et al [23], [24] and Sharma et al [25] proved various fixed point theorems using the concepts of semi-compatible mappings, property (E.A.)…”

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 Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces

Cited by 170 publications

References 40 publications

Common Fixed Point Theorems for Mappings under (CLRS)-Property in Partial Metric Spaces

Common Fixed Point Theorems for Mappings under (CLRS)-Property in Partial Metric Spaces

Irremissible stimulate on ‘Unified fixed point theorems in fuzzy metric spaces via common limit range property’

Fixed Points for Subsequential Continuous Mappings in Fuzzy Metric Space

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