A new contractive mapping principle in fuzzy metric spaces

Saha, P.; Choudhury, Binayak S.; Das, Pankaj

doi:10.1007/s40574-015-0044-y

Cited by 6 publications

(8 citation statements)

References 14 publications

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“…In 2015, Saha et al [12] introduced a new fuzzy contraction mapping and prove that such mappings have …xed point in complete fuzzy metric space-spaces. This contraction is called --fuzzy contraction.…”

Section: Preliminariesmentioning

confidence: 99%

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Fixed point theorems for single valued α-ψ-mappings in fuzzy metric spaces

Gupta¹,

Saini²,

Verma³

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Section: Preliminariesmentioning

confidence: 99%

“…Then the map f is said to be -admissible if (x; y; t) 1 ) (f x; f y; t) 1; 8 t > 0 and x; y 2 K: De…nition 2.6. [12] Let (K; M; ) be a fuzzy metric space and, let f : K ! K and ; : K K (0; 1) !…”

Section: De…nition 24 ([2]mentioning

confidence: 99%

Fixed point theorems for single valued α-ψ-mappings in fuzzy metric spaces

Gupta¹,

Saini²,

Verma³

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…After that, the fuzzy ideas appeared in many branches of mathematics through the work of the researchers over the years. In particular, FMSs [13] have been studied extensively by many authors in many mathematical disciplines because it has a naturally defined Hausdorff topology which is in a large way the cause for the successful improvement of metric FP theory in these spaces, some examples of these works were provided by [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces

Hammad

Sen

2021

Symmetry

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In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ−norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed.

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“…Today, fuzzy fixed point theory is a subject by itself regarding the multifacet development that it has undergone. Some instances of these works are [7][8][9][10][11].…”

Section: Introduction and Mathematical Preliminariesmentioning

confidence: 99%

Determining Fuzzy Distance between Sets by Application of Fixed Point Technique Using Weak Contractions and Fuzzy Geometric Notions

et al. 2019

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In the present paper, we solve the problem of determining the fuzzy distance between two subsets of a fuzzy metric space. We address the problem by reducing it to the problem of finding an optimal approximate solution of a fixed point equation. This approach is well studied for the corresponding problem in metric spaces and is known as proximity point problem. We employ fuzzy weak contractions for that purpose. Fuzzy weak contraction is a recently introduced concept intermediate to a fuzzy contraction and a fuzzy non-expansive mapping. Fuzzy versions of some geometric properties essentially belonging to Hilbert spaces are considered in the main theorem. We include an illustrative example and two corollaries, one of which comes from a well-known fixed point theorem. The illustrative example shows that the main theorem properly includes its corollaries. The work is in the domain of fuzzy global optimization by use of fixed point methods.

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A new contractive mapping principle in fuzzy metric spaces

Cited by 6 publications

References 14 publications

Fixed point theorems for single valued α-ψ-mappings in fuzzy metric spaces

Fixed point theorems for single valued α-ψ-mappings in fuzzy metric spaces

A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces

Determining Fuzzy Distance between Sets by Application of Fixed Point Technique Using Weak Contractions and Fuzzy Geometric Notions

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