Abstract
By using the weaker Meir-Keeler functionϕand the triangularα-admissible mappingα, we introduce the notion of(α-ϕ)-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces.
Highlights
Introduction and PreliminariesLet X be a nonempty set and let d : X × X → [0, ∞)
By using the weaker Meir-Keeler function φ and the triangular α-admissible mapping α, we introduce the notion of (α − φ)-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces
We introduce the new notion of generalized quasimetric space as follows
Summary
Introduction and PreliminariesLet X be a nonempty set and let d : X × X → [0, ∞). d is called a distance function if for every x, y, z ∈ X, satisfies (d1) d(x, x) = 0; (d2) d(x, y) = d(y, x) = 0 ⇒ x = y; (d3) d(x, y) = d(y, x); (d4) d(x, z) ≤ d(x, y) + d(y, z).If d satisfies conditions (d1)–(d4), d is called a metric on X. By using the weaker Meir-Keeler function φ and the triangular α-admissible mapping α, we introduce the notion of (α − φ)-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces.
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