Email this article Perturbation of the fixed point problem for continuous mappings
- Authors: Zhukovskaya Z.T.1, Zhukovskiy S.E.1
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Affiliations:
- V. A. Trapeznikov Institute of Control Sciences of RAS
- Issue: Vol 26, No 135 (2021)
- Pages: 241-249
- Section: Articles
- URL: https://bakhtiniada.ru/2686-9667/article/view/294993
- DOI: https://doi.org/10.20310/2686-9667-2021-26-135-241-249
- ID: 294993
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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.
About the authors
Zukhra T. Zhukovskaya
V. A. Trapeznikov Institute of Control Sciences of RAS
Email: zyxra2@yandex.ru
Candidate of Physics and Mathematics, Leading Researcher 65 Profsoyuznaya St., Moscow 117997, Russian Federation
Sergey E. Zhukovskiy
V. A. Trapeznikov Institute of Control Sciences of RAS
Email: s-e-zhuk@yandex.ru
Doctor of Physics and Mathematics, Leading Researcher 65 Profsoyuznaya St., Moscow 117997, Russian Federation
References
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- A.V. Arutyunov, E.R. Avakov, S.E. Zhukovskiy, “Stability theorems for estimating the distance to a set of coincidence points”, SIAM Journal on Optimization, 25:2 (2015), 807-828.
- Р.Р. Ахмеров, М.И. Каменский, А.С. Потапов, Б.Н. Садовский, “Уплотняющие операторы”, Итоги науки и техн. Сер. Мат. анал., 18, ВИНИТИ, М., 1980, 185-250.
- J. Diestel, Sequences and Series in Banach Spaces, Graduate Texts in Mathematics, Springer-Verlag, New York, 1984, 263 pp.
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