Email this article Kantorovich’s Fixed Point Theorem in Metric Spaces and Coincidence Points
- Authors: Arutyunov A.V.1,2,3, Zhukovskiy E.S.4, Zhukovskiy S.E.2,3,5
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Affiliations:
- Institute for Information Transmission Problems (Kharkevich Institute)
- V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
- People’s Friendship University of Russia (RUDN University)
- Derzhavin Tambov State University
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 304, No 1 (2019)
- Pages: 60-73
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/175736
- DOI: https://doi.org/10.1134/S008154381901005X
- ID: 175736
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Abstract
Existence and uniqueness theorems are obtained for a fixed point of a mapping from a complete metric space to itself. These theorems generalize the theorems of L. V. Kantorovich for smooth mappings of Banach spaces. The results are extended to the coincidence points of both ordinary and set-valued mappings acting in metric spaces.
About the authors
A. V. Arutyunov
Institute for Information Transmission Problems (Kharkevich Institute); V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences; People’s Friendship University of Russia (RUDN University)
Author for correspondence.
Email: arutyunov@cs.msu.ru
Russian Federation, Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051; Profsoyuznaya ul. 65, Moscow, 117997; ul. Miklukho-Maklaya 6, Moscow, 117198
E. S. Zhukovskiy
Derzhavin Tambov State University
Author for correspondence.
Email: zukovskys@mail.ru
Russian Federation, Internatsional’naya ul. 33, Tambov, 392000
S. E. Zhukovskiy
V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences; People’s Friendship University of Russia (RUDN University); Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: s-e-zhuk@yandex.ru
Russian Federation, Profsoyuznaya ul. 65, Moscow, 117997; ul. Miklukho-Maklaya 6, Moscow, 117198; Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701
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