On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces

Sen, Manuel De la; Abbas, Mujahid; Saleem, Naeem

doi:10.3390/math5020022

Cited by 11 publications

(8 citation statements)

References 44 publications

(52 reference statements)

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“…Note: Analogous to the above definition, there are notions of A 0 (t) and B 0 (t) that have been used in fuzzy proximity point problems in work [20,33]. The difference with the above definition is that they are independent from the parameter t here.…”

Section: Lemma 2 ([32]mentioning

confidence: 99%

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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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Section: Lemma 2 ([32]mentioning

confidence: 99%

“…The corresponding problem in the fuzzy metric space was considered in recent works like [20][21][22][23]. As in the case of the problem in metric spaces, it should be possible to solve the problem by applying contractions of various types.…”

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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“…This work has been appreciated by researchers (see [9,10]). This work was extended by several researchers in various ways (compare with [11][12][13][14][15][16][17][18][19][20][21]). Among one of them, in 1969, Nadler proposed Banach's contraction principle for correspondence in Hausdorff metric spaces (see [22]).…”

Section: Introductionmentioning

confidence: 99%

Fuzzy b-Metric Spaces: Fixed Point Results for ψ-Contraction Correspondences and Their Application

Abbas

Lael

Saleem

2020

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In this paper we introduce the concepts of ψ -contraction and monotone ψ -contraction correspondence in “fuzzy b -metric spaces” and obtain fixed point results for these contractive mappings. The obtained results generalize some existing ones in fuzzy metric spaces and “fuzzy b -metric spaces”. Further we address an open problem in b -metric and “fuzzy b -metric spaces”. To elaborate the results obtained herein we provide an example that shows the usability of the obtained results.

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“…The application of this principle is not limited to these areas, it is extensively used in dynamically programming ( [3]) and biosciences as well. Due to wide range of applications, researchers around the globe are attracted towards this principle to generalize, modify and extend this pioneer result (for detail, see [4][5][6][7][8][9][10][11][12]). These modifications are consisting upon three pillars (1) generalizing the contractive conditions, (2) generalizing the underlying space and (3) modifying the single valued mapping with multivalued mapping.…”

Section: Introductionmentioning

confidence: 99%

Some New Results on Coincidence Points for Multivalued Suzuki-Type Mappings in Fairly Complete Spaces

2020

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In this paper, we introduce Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. We establish some coincidence and best proximity point results in fairly complete spaces. Also, we provide coincidence and best proximity point results in partially ordered complete metric spaces for Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. Furthermore, some examples are presented in each section to elaborate and explain the usability of the obtained results. As an application, we obtain fixed-point results in metric spaces and in partially ordered metric spaces. The results obtained in this article further extend, modify and generalize the various results in the literature.

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On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces

Cited by 11 publications

References 44 publications

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

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

Fuzzy b-Metric Spaces: Fixed Point Results for ψ-Contraction Correspondences and Their Application

Some New Results on Coincidence Points for Multivalued Suzuki-Type Mappings in Fairly Complete Spaces

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