Best Proximity Point Results in Non-Archimedean Modular Metric Space

Paknazar, Mohadeshe; Sen, Manuel De la

doi:10.3390/math5020023

Cited by 2 publications

(1 citation statement)

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“…Although the convexity of a modular metric brings considerable advantages, the absence of the triangle inequality generates major difficulties when trying to expand some results to the modular setting. A possible solution was provided by Paknazar in [12,13] by defining the so-called non-Archimedean metric modular. In fact, the new modular proves to be a parameterized family of classical metrics; therefore, for each value of the parameter, the triangle inequality or the continuity is ensured.…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Points Results on Non-Archimedean Metric Modular Spaces

Kassab

2019

Symmetry

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This paper introduces two new contractive conditions in the setting of non-Archimedean modular spaces, via a C-class function, an altering distance function, and a control function. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. The main outcomes provide sufficient conditions for the existence of common fixed points for four mappings. Examples are provided in order to prove the usability of the theoretical approach. Moreover, these examples use a non-Archimedean metric modular, which is not convex, making the study of nonconvex modulars more appealing.

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Section: Introductionmentioning

confidence: 99%

Common Fixed Points Results on Non-Archimedean Metric Modular Spaces

Kassab

2019

Symmetry

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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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Best Proximity Point Results in Non-Archimedean Modular Metric Space

Cited by 2 publications

References 20 publications

Common Fixed Points Results on Non-Archimedean Metric Modular Spaces

Common Fixed Points Results on Non-Archimedean Metric Modular Spaces

Property P in modular metric spaces

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