Email this article Existence of a coincidence point in a critical case when the covering constant and the Lipschitz constant are equal
- Authors: ARUTYUNOV A.V.1,2, VASYANIN O.A.1,2
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Affiliations:
- Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences
- Lomonosov Moscow State University
- Issue: Vol 30, No 151 (2025)
- Pages: 209-217
- Section: Original articles
- URL: https://journals.rcsi.science/2686-9667/article/view/324416
- ID: 324416
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Abstract
We consider two mappings acting between metric spaces and such that one of them is covering and the other satisfies the enhanced Lipschitz property. It is assumed here that the covering constant and the Lipschitz constant of these mappings are equal. We prove the result of the existence of a coincidence point of single-valued mappings in the case when the series of iterations of the function that provides execution of the enhanced Lipschitz property converges. We prove the similar result for set-valued mappings. We provide examples of functions for which the series of their iterations converges or diverges.
About the authors
Aram V. ARUTYUNOV
Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences; Lomonosov Moscow State University
Author for correspondence.
Email: arutyunov@cs.msu.ru
ORCID iD: 0000-0001-7326-7492
Doctor of Physical and Mathematical Sciences, Chief Researcher of Laboratory 45; Professor
Russian Federation, 65 Profsoyuznaya St., Moscow 117997, Russian Federation; 1 Leninskie Gory, Moscow 119991, Russian FederationOleg A. VASYANIN
Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences; Lomonosov Moscow State University
Email: o.vasyanin@gmail.com
ORCID iD: 0009-0008-5088-8809
Engineer of Laboratory 45; Student
Russian Federation, 65 Profsoyuznaya St., Moscow 117997, Russian Federation; 1 Leninskie Gory, Moscow 119991, Russian FederationReferences
- A.V. Arutyunov, "Covering mappings in metric spaces and fixed points", Dokl. Math., 76 (2007), 665-668.
- A.V. Arutyunov, "Caristi's condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points", Proc. Steklov Inst. Math., 291 (2015), 24-37.
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