Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces

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

doi:10.3390/math7040327

Cited by 7 publications

(5 citation statements)

References 23 publications

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“…Zadeh [36] introduced the concept of a fuzzy set, back in 1965, as an extension of a crisp set where each element of a set has some membership values between [0, 1]. Since then, several mathematical structures have been transformed to fuzzy sets, see ( [1], [9], [13], [19], [30], [32], [34]). Kramosil and Michálek [21] applied this theory to metric spaces and defined fuzzy metric space which could be viewed as a reformulation of statistical metric spaces [25].…”

Section: Introductionmentioning

confidence: 99%

WITHDRAWN: Extended Rectangular Fuzzy B-metric Space

Furqan¹,

Saleem²,

Abbas

2021

Preprint

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In this paper, we introduce an extended rectangular fuzzy b-metric space which generalizes rectangular fuzzy b-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy b-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where a Ciric type contraction was employed. Our main result generalizes some comparable results in rectangular fuzzy b-metric space and rectangular fuzzy metric space. We provide some examples to support the concepts and results presented herein. As an application of our result, we obtain the existence of the solution of the integral equation.

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Section: Introductionmentioning

confidence: 99%

WITHDRAWN: Extended Rectangular Fuzzy B-metric Space

Furqan¹,

Saleem²,

Abbas

2021

Preprint

Self Cite

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“…Mehmood et al [14] presented the notion of fuzzy extended b-metric spaces (FEBMSs) by replacing the coefficient b ≥ 1 with a function α : D × D → [1, ∞). The approach of intuitionistic fuzzy metric spaces was tossed by Park et al [15][16][17][18], Saleem et al [19][20][21][22][23][24][25][26][27][28] proved several fixed theorems on intuitionistic fuzzy metric space. Sintunavarat et al [29] established various fixed theorems for a generalized intuitionistic fuzzy contraction in intuitionistic fuzzy metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Unique Solution of Integral Equations via Intuitionistic Extended Fuzzy b-Metric-Like Spaces

Saleem¹,

Javed²,

Uddin³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In this manuscript, our goal is to introduce the notion of intuitionistic extended fuzzy b-metric-like spaces. We establish some fixed point theorems in this setting. Also, we plot some graphs of an example of obtained result for better understanding. We use the concepts of continuous triangular norms and continuous triangular conorms in an intuitionistic fuzzy metric-like space. Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions. Triangular conorms are known as dual operations of triangular norms. The obtained results boost the approaches of existing ones in the literature and are supported by some examples and applications.

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“…In 1965, Zadeh [12] defined a fuzzy set that generalizes the definition of a crisp set by associating all elements with membership values between the interval ½0, 1. Since then, the fuzzy set theory has been used extensively in mathematics ( [13][14][15][16][17][18]) and many other areas ( [19][20][21]). The definition of fuzzy metric space was given by Kramosil and Michálek [22] in 1975.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results

Furqan

Işık

Saleem

2021

Journal of Function Spaces

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In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b -metric space, fuzzy b -metric space, and extended fuzzy b -metric space. We use f , g , h , three noncomparable functions as follows: m q μ , η , t + s + w ≥ m q μ , ν , t / f μ , ν ∗ m q ν , ξ , s / g ν , ξ ∗ m q ξ , η , w / h ξ , η . We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to support our main results. We also apply our technique to the uniqueness for the solution of an integral equation.

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Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces

Cited by 7 publications

References 23 publications

WITHDRAWN: Extended Rectangular Fuzzy B-metric Space

WITHDRAWN: Extended Rectangular Fuzzy B-metric Space

Unique Solution of Integral Equations via Intuitionistic Extended Fuzzy b-Metric-Like Spaces

Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results

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