Some new approaches to modular and fuzzy metric and related best proximity results

Paknazar, Mohadeseh; Sen, Manuel De la

doi:10.1016/j.fss.2019.12.012

Cited by 4 publications

(2 citation statements)

References 13 publications

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“…Furthermore, when the mapping in question is self-mapping, ℬ𝒫𝒫-theorem yields a fixed point result. References [14][15][16][17] and the references therein provide some results in this approach.…”

Section: Introductionmentioning

confidence: 99%

Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space

Sabri

Ahmed²

2023

Baghdad Sci.J

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The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced. After that, the best proximity point theorem for such type of mapping in a fuzzy normed space is state and prove. In addition, the idea of α ̃–ϕ ̃-proximal contractive mapping is presented in a fuzzy normed space and under specific conditions, the best proximity point theorem for such type of mappings is proved. Furthermore, some examples are offered to show the results' usefulness.

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Section: Introductionmentioning

confidence: 99%

Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space

Sabri

Ahmed²

2023

Baghdad Sci.J

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“…Indeed, we look at these spaces as a nonlinear version of the classical modular spaces introduced by H. Nakano (Nakano, 1950) on vector spaces and modular function spaces introduced by (Musielak, 1983) and (Orlicz, 1988a(Orlicz, , 1988b. More about modular metric spaces can be read in (Hussain et al, 2011), (Paknazar & De la Sen, 2017) and (Paknazar & De la Sen, 2020).…”

Section: Introductionmentioning

confidence: 99%

Property P in modular metric spaces

Paunović¹,

Kumar²,

Malik³

et al. 2022

Vojnotehnički glasnik

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Introduction/purpose: The aim of this paper is to present the concept of the generalized ∅-weak contractive condition involving various combinations of d(x,y) in modular metric spaces. Methods: Conventional theoretical methods of functional analysis. Results: This study presents the result of (Murthy & Vara Prasad, 2013) for a single-valued mapping satisfying a generalized ∅ -weak contractive condition involving various combinations of d(x,y). It is generalized in the setting of modular metric spaces, and then it is proved that this single-valued map satisfies the property P. In the end, an example is given in support of the result. Conclusion: With proper generalisations, it is possible to formulate well-known results of classical metric spaces to the case of modular metric spaces.

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Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems

Panda¹,

Ravichandran²,

Hazarika

2021

Chaos, Solitons & Fractals

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Some new approaches to modular and fuzzy metric and related best proximity results

Cited by 4 publications

References 13 publications

Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space

Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space

Property P in modular metric spaces

Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems

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