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Russian Universities Reports. Mathematics, 2021, Volume 26, Issue 135, Pages 241–249
DOI: https://doi.org/10.20310/2686-9667-2021-26-135-241-249
(Mi vtamu229)
 

This article is cited in 1 scientific paper (total in 1 paper)

Scientific articles

Perturbation of the fixed point problem for continuous mappings

Z. T. Zhukovskaya, S. E. Zhukovskiy

V. A. Trapeznikov Institute of Control Sciences of RAS
Full-text PDF (480 kB) Citations (1)
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Abstract: We consider the problem of a double fixed point of pairs of continuous mappings defined on a convex closed bounded subset of a Banach space. It is shown that if one of the mappings is completely continuous and the other is continuous, then the property of the existence of fixed points is stable under contracting perturbations of the mappings. We obtain estimates for the distance from a given pair of points to double fixed points of perturbed mappings. We consider the problem of a fixed point of a completely continuous mapping on a convex closed bounded subset of a Banach space. It is shown that the property of the existence of a fixed point of a completely continuous map is stable under contracting perturbations. Estimates of the distance from a given point to a fixed point are obtained. As an application of the obtained results, the solvability of a difference equation of a special type is proved.
Keywords: double fixed point, fixed point, completely continuous mapping, continuous mapping, difference equation.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00080_а
Ministry of Science and Higher Education of the Russian Federation МД-2658.2021.1.1
The work is supported by the Russian Foundation for Basic Research (project no. 19-01-00080_а) and by a grant from the President of the Russian Federation (project no. MD-2658.2021.1.1).
Received: 26.04.2021
Document Type: Article
UDC: 517
Language: Russian
Citation: Z. T. Zhukovskaya, S. E. Zhukovskiy, “Perturbation of the fixed point problem for continuous mappings”, Russian Universities Reports. Mathematics, 26:135 (2021), 241–249
Citation in format AMSBIB
\Bibitem{ZhuZhu21}
\by Z.~T.~Zhukovskaya, S.~E.~Zhukovskiy
\paper Perturbation of the fixed point problem for continuous mappings
\jour Russian Universities Reports. Mathematics
\yr 2021
\vol 26
\issue 135
\pages 241--249
\mathnet{http://mi.mathnet.ru/vtamu229}
\crossref{https://doi.org/10.20310/2686-9667-2021-26-135-241-249}
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    Russian Universities Reports. Mathematics
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