Abstract
In this paper, we investigate the existence and the uniqueness of a common fixed point of a pair of self-mappings satisfying new contractive type conditions on a modular metric space endowed with a reflexive digraph. An application is given to show the use of our main result.
Highlights
Introduction and preliminariesMore generalized contractive type conditions are considered in the study of the existence and uniqueness of the fixed point
In this paper, motivated by some works as [10], we extend the following theorem to the setting of the modular metric space endowed with a reflexive digraph
We investigate the existence and uniqueness of the common fixed point of a pair of mappings satisfying a generalized contractive condition in the setting of a modular metric space with a reflexive digraph
Summary
Introduction and preliminariesMore generalized contractive type conditions are considered in the study of the existence and uniqueness of the fixed point. Definition 1.1 ([7]) A function ω : ]0, +∞[ × X × X → [0, +∞] is said to be modular metric on X if it satisfies the following conditions: (i) Given x, y ∈ X, x = y if and only if ωλ(x, y) = 0 for all λ > 0; (ii) For all x, y ∈ X, for all λ > 0, ωλ(x, y) = ωλ(y, x); (iii) For all x, y, z ∈ X and for all λ, μ > 0, ωλ+μ(x, y) ≤ ωλ(x, z) + ωμ(z, y).
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