Existence and Uniqueness of a Common Best Proximity Point on Fuzzy Metric Space

In this paper, we introduce fuzzy multiplicative metric space and prove some best proximity point theorems for single-valued and multivalued proximal contractions on the newly introduced space. As corollaries of our results, we prove some fixed-point theorems. Also, we present best proximity point theorems for Feng-Liu-type multivalued proximal contraction in fuzzy metric space. Moreover, we illustrate our results with some interesting examples.

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Some results on common best proximity point in fuzzy metric

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v35i2.29466 ◽

2017 ◽

Vol 35 (2) ◽

pp. 177-194 ◽

Cited By ~ 2

Author(s):

Hamid Shayanpour ◽

Asiyeh Nematizadeh

Keyword(s):

Metric Space ◽

Best Proximity Point ◽

Fuzzy Metric ◽

Common Best Proximity Point

In this paper, we dene the concepts of commute proximally, dominate prox-imally, weakly dominate proximally and common best proximity point in fuzzy metricspace (abbreviated, FM-space). We prove some common best proximity point and com-mon xed point theorems for dominate proximally and weakly dominate proximally map-pings in FM-space under certain conditions. Our results generalize many known resultsin metric space.

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Common Best Proximity Point Theorems in JS-Metric Spaces Endowed with Graphs

Journal of Function Spaces ◽

10.1155/2021/5524494 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Chaiporn Thangthong ◽

Phakdi Charoensawan ◽

Supreedee Dangskul ◽

Narawadee Phudolsitthiphat

Keyword(s):

Binary Relation ◽

Directed Graph ◽

Metric Space ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Best Proximity Point ◽

Edge Preserving ◽

Common Best Proximity Point ◽

Existence And Uniqueness Results ◽

Uniqueness Results

In this paper, we introduce a notion of G -proximal edge preserving and dominating G -proximal Geraghty for a pair of mappings, which will be used to present some existence and uniqueness results for common best proximity points. Here, the mappings are defined on subsets of a JS-metric space endowed with a directed graph. An example is also provided to support the results. Moreover, we apply our result to a similar setting, where the JS-metric space is endowed with a binary relation.

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Fixed Point Theorem in Fuzzy Metric Space Satisfying Integral Inequality

International Journal of Scientific Research ◽

10.15373/22778179/feb2014/96 ◽

2012 ◽

Vol 3 (2) ◽

pp. 305-307

Author(s):

Geeta Modi ◽

◽

Arvind Gupta ◽

Varun Singh

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Space ◽

Integral Inequality ◽

Fuzzy Metric Space ◽

Fuzzy Metric

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Schauder Fixed Point Theorems in Intuitionistic Fuzzy Metric Space

Iraqi Journal of Science ◽

10.24996/ijs.2017.58.1c.12 ◽

2017 ◽

Vol 58 (1C) ◽

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Fuzzy Metric Space ◽

Fuzzy Metric ◽

Intuitionistic Fuzzy ◽

Schauder Fixed Point

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Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

Journal of Applied Mathematics ◽

10.1155/2014/150941 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 4

Author(s):

Erdal Karapınar ◽

V. Pragadeeswarar ◽

M. Marudai

Keyword(s):

Approximate Solution ◽

Metric Space ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Best Proximity Point ◽

Complete Metric Space ◽

Optimal Approximate Solution ◽

Weak Contraction ◽

Complete Metric Spaces ◽

New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

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