(q1, q2)-QUASIMETRIC SPACES. COVERING AND COINCIDENCE POINTS. A REVIEW RESULTS Full article
| Journal |
Fixed Point Theory
ISSN: 1583-5022 , E-ISSN: 2066-9208 |
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| Output data | Year: 2022, Volume: 23, Number: 2, Pages: 473-486 Pages count : 14 DOI: 10.24193/fpt-ro.2022.2.03 | ||||
| Tags | (q1; coincidence points; contraction mapping; covering mapping; f-quasimetric space; fixed point; Hausdorff deviation; Lipschitz mapping; multivalued mapping; q2)-quasimetric space | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 22-21-00863 |
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, Lp-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 gener-alizing Banach’s fixed point theorem to such spaces. The present paper is a review of these results. © 2022, House of the Book of Science. All rights reserved.
Cite:
Arutyunov A.V.
, Greshnov A.V.
(q1, q2)-QUASIMETRIC SPACES. COVERING AND COINCIDENCE POINTS. A REVIEW RESULTS
Fixed Point Theory. 2022. V.23. N2. P.473-486. DOI: 10.24193/fpt-ro.2022.2.03 WOS Scopus РИНЦ OpenAlex
(q1, q2)-QUASIMETRIC SPACES. COVERING AND COINCIDENCE POINTS. A REVIEW RESULTS
Fixed Point Theory. 2022. V.23. N2. P.473-486. DOI: 10.24193/fpt-ro.2022.2.03 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 25, 2021 |
| Accepted: | Feb 4, 2022 |
Identifiers:
| Web of science: | WOS:000921038000003 |
| Scopus: | 2-s2.0-85134164957 |
| Elibrary: | 59278498 |
| OpenAlex: | W4365402273 |