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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 11, Pages 1711–1723
DOI: https://doi.org/10.7868/S0044466914110118 (Mi zvmmf10107) 		 
First-order regularization methods for accretive inclusions in a Banach space

I. P. Ryazantseva

Nizhni Novgorod State Technical University, ul. Minina 24, Nizhni Novgorod, 603600, Russia
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DOI: https://doi.org/10.7868/S0044466914110118
Abstract: Equations with set-valued accretive operators in a Banach space are considered. Their solutions are understood in the sense of inclusions. By applying the resolvent of the set-valued part of the equation operator, these equations are reduced to ones with single-valued operators. For the constructed problems, a regularized continuous method and a regularized first-order implicit iterative process are proposed. Sufficient conditions for their strong convergence are obtained in the case of approximately specified data.
Key words: accretive operator, $m$-accretive operator, inversely strongly pseudoaccretive operator, resolvent, regularization, continuous method, iterative method, convergence.
Received: 10.11.2013
Revised: 28.04.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 11, Pages 1647–1658
DOI: https://doi.org/10.1134/S0965542514110116
Bibliographic databases:
Document Type: Article
UDC: 519.642.8
Language: Russian
Citation: I. P. Ryazantseva, “First-order regularization methods for accretive inclusions in a Banach space”, Zh. Vychisl. Mat. Mat. Fiz., 54:11 (2014), 1711–1723; Comput. Math. Math. Phys., 54:11 (2014), 1647–1658
Citation in format AMSBIB
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