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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. Arutyunovabc, E. S. Zhukovskiyd, S. E. Zhukovskiyebc 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
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.
Received: August 20, 2018 Revised: September 25, 2018 Accepted: November 19, 2018
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
Linking options:
https://www.mathnet.ru/eng/tm3962https://doi.org/10.4213/tm3962 https://www.mathnet.ru/eng/tm/v304/p68
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