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L-Fuzzy fixed point results in ℱ -metric spaces with applications

Lateef Durdana

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20220206

Jleli and Samet in [On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018), 128 (20 pages)] introduced the notion of ℱ -metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of this generalized metric space. The objective of this article is to use ℱ -metric space and establish some common fixed point theorems for (β-ψ)-contractions. Our results expand, generalize, and consolidate several known results in the literature. As applications of the main result, the solution for fuzzy initial-value problems in the background of a generalized Hukuhara derivative was discussed.

Best proximity points in ℱ-metric spaces with applications

Lateef Durdana

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220191

The aim of this article is to introduce α - ψ -proximal contraction in the setting of ℱ-metric space and prove the existence of best proximity points for these contractions. As applications of our main results, we obtain coupled best proximity points on ℱ-metric space equipped with an arbitrary binary relation.