The recent articles of Arutyunov and Greshnov extend the Banach and Hadler Fixed-Point Theorems and the Arutyunov Coincidence-Point Theorem to the mappings of (q1, q2)-quasimetric spaces. This article addresses similar questions for f-quasimetric spaces.
Given a function f: R +2 → R+ with f(r1, r2) → 0 as (r1, r2) → (0, 0), an f-quasimetric space is a nonempty set X with a possibly asymmetric distance function ρ: X2 → R+ satisfying the f-triangle inequality: ρ(x, z) ≤ f(ρ(x, y), ρ(y, z)) for x, y, z ∈ X. We extend the Banach Contraction Mapping Principle, as well as Krasnoselskii’s and Browder’s Theorems on generalized contractions, to mappings of f-quasimetric spaces.
f-quasimetric asymptotic triangle inequality fixed point generalized contraction
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