Theorems on Soft Fuzzy Metric Spaces by Using Control Function

Khandait, Sneha A.; Singh, Chitra; Bhardwaj, Ramakant; Mishra, Amit

doi:10.1002/9781119763437.ch15

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2023

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“…In 2017, Ferhan Sola Erduran [8] proposed the idea of a soft fuzzy metric with fundamental characteristics and topological structure in soft fuzzy metric spaces by applying the concepts of soft points and soft real numbers. The study was further explored by introducing concepts such as countability, convergence, and completeness in soft fuzzy metric spaces, compact soft fuzzy metric spaces, and totally fuzzy bounded spaces [6,[28][29][30]. Any version of the Banach contraction principle has not been proven in a soft fuzzy metric space.…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Results in Soft Fuzzy Metric Spaces

2023

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The primary objective of the paper is to present the Banach contraction theorem in soft fuzzy metric spaces while taking into consideration a restriction on the soft fuzzy metric between the soft points of the absolute soft set. A new altering distance function, namely the Ψ-contraction function, is introduced on soft fuzzy metric spaces, and some fixed point results are proven by considering soft mappings that comprise Ψ-contraction with the continuity of soft t-norm. In addition to that, some illustrations are supplied for the support of the established soft fuzzy Banach contraction theorem and fixed point results over Ψ-contraction mappings. The obtained results generalize and extend some well-known results present in the literature on fixed point theory.

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Section: Introductionmentioning

confidence: 99%