A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Kantorovich's Fixed Point Theorem in Metric Spaces and Coincidence Points”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 68–82; Proc. Steklov Inst. Math., 304 (2019), 60

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 304, Pages 68–82
DOI: https://doi.org/10.4213/tm3962 (Mi tm3962)

This article is cited in 8 scientific papers (total in 8 papers)

Kantorovich's Fixed Point Theorem in Metric Spaces and Coincidence Points

A. V. Arutyunov^abc, E. S. Zhukovskiy^d, S. E. Zhukovskiy^ebc

^a Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia
^b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Profsoyuznaya ul. 65, Moscow, 117997 Russia
^c People's Friendship University of Russia (RUDN University), ul. Miklukho-Maklaya 6, Moscow, 117198 Russia
^d Derzhavin Tambov State University, Internatsional'naya ul. 33, Tambov, 392000 Russia
^e Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia

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DOI: https://doi.org/10.4213/tm3962

Abstract: Existence and uniqueness theorems are obtained for a fixed point of a mapping of a complete metric space into itself, that generalize the theorems of L. V. Kantorovich for smooth mappings of Banach spaces. These results are extended to the coincidence points of both ordinary and maultivalued mappings acting in metric spaces.

Funding agency	Grant number
Ministry of Education and Science of the Russian Federation	1.962.2017/4.6 3.8515.2017/БЧ
Russian Foundation for Basic Research	17-51-12064 17-41-680975 18-01-00106 19-01-00080
This work was supported by the Ministry of Education and Science of the Russian Federation (project nos. 1.962.2017/4.6 and 3.8515.2017/BCh) and by the Russian Foundation for Basic Research (project nos. 17-51-12064, 17-41-680975, 18-01-00106, and 19-01-00080).

Received: August 20, 2018
Revised: September 25, 2018
Accepted: November 19, 2018

English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 304, Pages 60–73
DOI: https://doi.org/10.1134/S008154381901005X

Bibliographic databases:

Document Type: Article

UDC: 517+515.126.4

Language: Russian

Citation: A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Kantorovich's Fixed Point Theorem in Metric Spaces and Coincidence Points”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 68–82; Proc. Steklov Inst. Math., 304 (2019), 60–73

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This publication is cited in the following 8 articles:

E. S. Zhukovskiy, E. A. Panasenko, “The method of comparison with a model equation in the study of inclusions in vector metric spaces”, Proc. Steklov Inst. Math. (Suppl.), 325, suppl. 1 (2024), S239–S254
E. Zhukovskiy, E. Panasenko, “Extension of the Kantorovich theorem to equations in vector metric spaces: applications to functional differential equations”, Mathematics, 12:1 (2023), 64
A. .V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, Z. T. Zhukovskaya, “Kantorovich's fixed point theorem and coincidence point theorems for mappings in vector metric spaces”, Set-Valued Var. Anal., 30:2 (2022), 397–423
D. Sharma, S. K. Sunanda, S. K. Parhi, “Convergence of Traub's iteration under $\omega$ continuity condition in Banach spaces”, Russian Math. (Iz. VUZ), 65:9 (2021), 52–68
A. V. Arutyunov, S. E. Zhukovskiy, “Covering Mappings Acting into Normed Spaces and Coincidence Points”, Proc. Steklov Inst. Math., 315 (2021), 13–18
A. V. Arutyunov, S. E. Zhukovskiy, “On exact penalties for constrained optimization problems in metric spaces”, Eurasian Math. J., 12:4 (2021), 10–20
E. S. Zhukovskiy, “Comparison Method for Studying Equations in Metric Spaces”, Math. Notes, 108:5 (2020), 679–687
A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “On the stability of fixed points and coincidence points of mappings in the generalized Kantorovich's theorem”, Topology Appl., 275 (2020), 107030

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

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