Email this article On coincidence points in $(q_1, q_2)$-quasimetric space
- Authors: Benarab S.1,2, Merchela W.1,3,4, Kharoubi M.E.4, Khial N.3
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Affiliations:
- University Salah Boubnider Constantine 3
- Laboratory of Applied Mathematics and Modeling 8 May 1945 University
- Mustapha Stambouli University – Mascara
- Laboratory of Applied Mathematics and Modeling 8 May 1945 University
- Issue: Vol 30, No 152 (2025)
- Pages: 309-321
- Section: Original articles
- URL: https://journal-vniispk.ru/2686-9667/article/view/357012
- ID: 357012
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Abstract
In this paper, we present a theorem on a coincidence point of mappings which extends the Arutyunov theorem. The original version of the Arutyunov theorem guaranteed the existence of a coincidence point for two mappings acting in metric spaces, one of which is $\alpha$-covering and the other is $\beta$-Lipschitz, where $\alpha > \beta.$ This theorem was then extended to mappings acting in $(q_1, q_2)$-quasimetric spaces. In this paper, the problem of the existence of a coincidence point is solved for mappings acting from a $(q_1, q_2)$-quasimetric space to a set equipped with a distance satisfying only the identity condition (the distance vanishes if and only if the points coincide). Under conditions similar to those of the Arutyunov theorem, the existence of a coincidence point is proved. In addition, the questions of convergence of sequences of coincidence points of mappings $\psi_n, \varphi_n$ to the coincidence point $\xi$ of mappings $\psi, \varphi$ are investigated under the convergences $\psi_n(\xi)\to \psi(\xi),$ $\varphi_n(\xi)\to \varphi(\xi).$
About the authors
Sarra Benarab
University Salah Boubnider Constantine 3; Laboratory of Applied Mathematics and Modeling8 May 1945 University
Author for correspondence.
Email: benarab.sarraa@gmail.com
ORCID iD: 0000-0002-8849-8848
Candidate of Physical and Mathematical Sciences, Associate Professor, Faculty of Architecture and Urban Planning
Algeria, B.P. 72, Ali Mendjeli, El Khroub, Constantine 25016, Algeria; B.P. 401, Guelma 24000, AlgeriaWassim Merchela
University Salah Boubnider Constantine 3; Mustapha Stambouli University – Mascara; Laboratory of Applied Mathematics and Modeling 8 May 1945 University
Email: merchela.wassim@gmail.com
ORCID iD: 0000-0002-3702-0932
Candidate of Physical and Mathematical Sciences, Associate Professor, Faculty of Process Engineering
Algeria, B.P. 72, Ali Mendjeli, El Khroub, Constantine 25016, Algeria; B.P. 305, Route de Mamounia, Mascara, 29000, Algeria; B.P. 401, Guelma 24000, AlgeriaMohammed E. Kharoubi
Laboratory of Applied Mathematics and Modeling 8 May 1945 University
Email: kharoubi.mohammed.elamin@gmail.com
ORCID iD: 0009-0008-0030-6057
Post-Graduate Student, Laboratory of Applied Mathematics and Modeling
Algeria, B.P. 401, Guelma 24000, AlgeriaNaouel Khial
Mustapha Stambouli University – Mascara
Email: khialnaouel@gmail.com
Master’s Degree Student, Department of Mathematics
Algeria, B.P. 305, Route de Mamounia, Mascara, 29000, AlgeriaReferences
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