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First-order regularization methods for accretive inclusions in a Banach space

Research paper by I. P. Ryazantseva

Indexed on: 14 Nov '14Published on: 14 Nov '14Published in: Computational Mathematics and Mathematical Physics



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.