Fixed Points of Set-valued F-contraction Operators in Quasi-ordered Metric Spaces with an Application to Integral Equations

Abstract

In this paper, we prove some new fixed point theorems involving set-valued F-contractions in the setting of quasi-ordered metric spaces. Our results are significant since we present Banach contraction principle in a different manner from that which is known in the present literature. Some examples and an application to existence of solution of Volterra-type integral equation are given to support the obtained results

Relation-Preserving Functional Contractions Involving a Triplet of Auxiliary Functions with an Application to Integral Equations

“…Solutions of integral equations have been studied using fixed-point methods by various researchers, e.g., the authors of Refs. [26][27][28]. In this section, applying Theorems 1 and 6, we describe the existence and uniqueness of solutions of the following FIE:…”

A Fixed Point Approach to Lattice Fuzzy Set via F-Contraction

“…Example [27]. If F(a) = lna+a for all a > 0 and H : (CB(ψ)) 2 → [0,+∞] is the Hausdorff metric on CB(ψ), then F satisfies 1-3 and each mapping G : ψ → CB(ψ) is an F-contraction such that H(Gx,Gy)e H(Gx,Gy)−d(x,y) ≤ e−τd(x,y) for all x,y ∈ ψ.…”

“…Then, T has a unique fixed point x * ∈ X, and for every x 0 ∈ X, a sequence {T n x 0 } n∈N is convergent to x * . Ample research regarding the existence of FP and common FP for single-valued and set-valued mappings satisfying F-contraction has been conducted (see [22][23][24][25][26][27] and references therein).…”