On iterative methods for solving equations with covering mappings

In this paper we propose an iterative method for solving the equation Υ(x, x) = y, where the mapping Υ acts in metric spaces and is covering in the first argument and Lipschitzian in the second one. Each subsequent element xi+1 of the sequence of iterations is defined by the previous one as a solution to the equation Υ(x, xi) = yi, where yi can be an arbitrary point sufficiently close to y. Conditions for convergence and error estimates are obtained. The method proposed is an iterative development of the Arutyunov method for finding coincidence points of mappings. In order to determine xi+1 in practical implementation of the method in linear normed spaces, it is proposed to perform one step by using the Newton–Kantorovich method. The thus-obtained method of solving the equation of the form Υ(x, u) = ψ(x) − φ(u) coincides with the iterative method proposed by A.I. Zinchenko,M.A. Krasnosel’skii, and I.A. Kusakin. © 2016, Pleiades Publishing, Ltd.

Авторы
Zhukovskaya T.V.1 , Zhukovskii E.S. 2, 3
Редакторы
-
Издательство
Maik Nauka Publishing / Springer SBM
Номер выпуска
4
Язык
Английский
Страницы
277-287
Статус
Опубликовано
Подразделение
-
Номер
-
Том
9
Год
2016
Организации
  • 1 Tambov State Technical University, ul. Sovetskaya 106, Tambov, 392000, Russian Federation
  • 2 Derzhavin Tambov State University, ul. Internatsional’naya 33, Tambov, 392000, Russian Federation
  • 3 Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation
Ключевые слова
approximate solution; covering mappings in metric spaces; iterative methods for solving equations
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/3796/