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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2016, Volume 19, Number 4, Pages 357–369
DOI: https://doi.org/10.15372/SJNM20160402
(Mi sjvm623)
 

This article is cited in 3 scientific papers (total in 3 papers)

On iterative methods for solving equations with covering mappings

T. V. Zhukovskaiaa, E. S. Zhukovskiybc

a Tambov State Technical University, 106 Sovetskaya str., Tambov, 392000, Russia
b G. R. Derzhavin Tambov State University, 33 Internatsional'naya str., Tambov, 392000, Russia
c Peoples Friendship University of Russia, 6 Mikluho-Maklay str., Moscow, 117198, Russia
Full-text PDF (436 kB) Citations (3)
References:
Abstract: In this paper we propose an iterative method for solving the equation $\Upsilon(x,x)=y$, where a mapping $\Upsilon$ acts in metric spaces, is covering in the first argument and Lipschitzian in the second one. Each subsequent element $x_{i+1}$ of a sequence of iterations is defined by the previous one as a solution to the equation $\Upsilon(x,x_i)=y_i$, where $y_i$ can be an arbitrary point sufficiently close to $y$. The conditions for convergence and error estimates have been obtained. The method proposed is an iterative development of the Arutyunov method for finding coincidence points of mappings. In order to determine $x_{i+1}$ it is proposed to perform one step using the Newton–Kantorovich method or the practical implementation of the method in linear normed spaces. The obtained method of solving the equation of the form $\Upsilon(x,u)=\psi(x)-\phi(u)$ coincides with the iterative method proposed by A. I. Zinchenko, M. A. Krasnosel'skii, I. A. Kusakin.
Key words: iterative methods for solving equations, covering mappings in metric spaces, approximate solution.
Funding agency Grant number
Russian Science Foundation 15-11-10021
Received: 18.03.2015
Revised: 18.02.2016
English version:
Numerical Analysis and Applications, 2016, Volume 9, Issue 4, Pages 277–287
DOI: https://doi.org/10.1134/S1995423916040029
Bibliographic databases:
Document Type: Article
UDC: 519.642.8
Language: Russian
Citation: T. V. Zhukovskaia, E. S. Zhukovskiy, “On iterative methods for solving equations with covering mappings”, Sib. Zh. Vychisl. Mat., 19:4 (2016), 357–369; Num. Anal. Appl., 9:4 (2016), 277–287
Citation in format AMSBIB
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  • This publication is cited in the following 3 articles:
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