DOI: 10.24193/fpt-ro.2022.2.03

Authors: A.V. Arutyunov and A.V. Greshnov

Abstract: In their recent papers, A.V. Arutyunov and A.V. Greshnov introduced (q₁,q₂)-quasimetric spaces and studied their properties: investigated covering mappings between (q₁,q₂)-quasimetric spaces, established sufficient conditions for the existence of a coincidence point for two mappings acting between (q₁,q₂)-quasimetric spaces such that one is a covering mapping and the other is Lipschitz continuous, proved Banach's fixed point theorem, obtained generalizations for multivalued mappings. The class of (q₁,q₂)-quasimetric spaces is sufficiently wide; it includes quasimetric spaces, b-metric spaces, Carnot-Carathéodory spaces with Box-quasimetics, L_p-spaces with p ∈ (0,1), etc. The development of the theory of coincidence points of mappings on (q₁,q₂)-quasimetric spaces initiated interest in the study of more general f-quasimetric spaces and in generalizing Banach's fixed point theorem to such spaces. The present paper is a review of these results.

Key Words and Phrases: (q₁,q₂)-quasimetric space, covering mapping, coincidence points, Lipschitz mapping, contraction mapping, fixed point, multivalued mapping, Hausdorff deviation, f-quasimetric space.

2010 Mathematics Subject Classification: 54E35, 54H25, 54A20, 54E15.

Published on-line: June 15th, 2022.

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