Best proximity points in ℱ-metric spaces with applications

The aim of this article is to introduce α\alpha -ψ\psi -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

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

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

A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f ( x ) = x . (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach

New Fixed Point Theorems with Applications to Non-Linear Neutral Differential Equations

The aim of this study is to investigate the existence of solutions for a non-linear neutral differential equation with an unbounded delay. To achieve our goals, we take advantage of fixed point theorems for self-mappings satisfying a generalized ( α , φ ) rational contraction, as well as cyclic contractions in the context of F -metric spaces. We also supply an example to support the new theorem