A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Kantorovich's Fixed Point Theorem in Metric Spaces and Coincidence Points”, Trudy Mat. Inst. Steklova, 2019, Volume 304,Pages <nobr>68–82</nobr>

RUS ENG

JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2019 Volume 304, Pages 68–82 (Mi tm3962)

This article is cited 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

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.

UDC: 517+515.126.4

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

DOI: 10.4213/tm3962

English version: Proceedings of the Steklov Institute of Mathematics, 2019, 304, 60–73

Bibliographic databases:

© Steklov Math. Inst. of RAS, 2024