Email this article ABOUT ANTITONE PERTURBATIONS OF COVERING MAPPINGS OF ORDERED SPACES
- Authors: Zhukovskaia T.V.1, Zhukovskiy E.S.2,3
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Affiliations:
- Tambov State Technical University
- Tambov State University named after G.R. Derzhavin
- Peoples’ Friendship University of Russia
- Issue: Vol 21, No 2 (2016)
- Pages: 371-374
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/365074
- DOI: https://doi.org/10.20310/1810-0198-2016-21-2-371-374
- ID: 365074
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Abstract
We consider the problem of existence of a solution x to the equation ψx, x = y , where y is given, the mapping ψ(∙, ∙) acts in ordered spaces, is order-covering with respect to the first argument, and antitone with respect to the second one. The concept of order-covering used in the article was proposed in the joint works of A.V. Arutyunov, E.S. Zhukovskiy, S.E. Zhukovskiy regarding the studies of the mappings’ coincidence points.
About the authors
Tatyana Vladimirovna Zhukovskaia
Tambov State Technical University
Email: t_zhukovskaia@mail.ru
Candidate of Physics and Mathematics, Associated Professor of High Mathematics Department Tambov, the Russian Federation
Evgeny Semenovich Zhukovskiy
Tambov State University named after G.R. Derzhavin; Peoples’ Friendship University of Russia
Email: zukovskys@mail.ru
Doctor of Physics and Mathematics, Professor, Director of the Research Institute ofMathematics, Physics and Informatics; Doctor of Physics and Mathematics, Professor of the Department of Nonlinear Analysis and Optimization Tambov, the Russian Federation; Moscow, the Russian Federation
References
СПИСОК ЛИТЕРАТУРЫ Arutyunov A.V., Zhukovskiy E.S., Zhukovskiy S.E. Coincidence points principle for mappings in partially ordered spaces // Topology and its Applications. 2015. V. 179. № 1. P. 13-33. Арутюнов А.В., Жуковский Е.С., Жуковский С.Е. О точках совпадения отображений в частично упорядоченных пространствах // Доклады Академии наук. 2013. Т. 453. № 5. С. 475-478. Арутюнов А.В., Жуковский Е.С., Жуковский С.Е. Точки совпадения многозначных отображений в частично упорядоченных пространствах // Доклады Академии наук. 2013. Т. 453. № 6. С. 595-598. Granas A., Dugundji D. Fixed Point Theory // Springer-Verlag, New York. 2003. Люстерник Л.А., Соболев В.И. Краткий курс функциональ ного анализа. М.: Высшая школа, 1982. Колмогоров А.Н., Фомин С.В. Элементы теории функций и функционального анализа. М.: Наука, 1981.
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