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The Fixed Points of Contractions of f-Quasimetric Spaces

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Abstract

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.

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Authors and Affiliations

  1. Tambov State University named after G. R. Derzhavin, Tambov, Russia

    E. S. Zhukovskiy

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  1. E. S. Zhukovskiy
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Correspondence to E. S. Zhukovskiy.

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Original Russian Text © 2018 Zhukovskiy E.S.

__________

Tambov. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 6, pp. 1338–1350, November–December, 2018; DOI: 10.17377/smzh.2018.59.609.

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Zhukovskiy, E.S. The Fixed Points of Contractions of f-Quasimetric Spaces. Sib Math J 59, 1063–1072 (2018). https://doi.org/10.1134/S0037446618060095

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  • DOI: https://doi.org/10.1134/S0037446618060095

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