Fixed point theorems for generalized (αβ-γ)-contractions in F-metric spaces with applications

Abstract

The purpose of this paper is to define generalized (αβ-ψ)-contraction in the context of F-metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay v/(l) = ρ1(l)v(l) + L(v)L(l-ς(l) + ρ3(l)v/(l-ς(l), where ρ1(l), ρ2(l) are continuous, ρ3(l) is continuously differentiable and ς(l) > 0, for all l ∈ R and is twice continuously differentiable.