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

Abstract

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\beta -ψ\psi )-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.

Keywords

• ℱ-metric space
• fixed point
• β-admissible
• hukuhara derivative
• 47h10
• 54h25
• 65q10
• 65q30