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.
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Original Russian Text © I.P. Ryazantseva, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 11, pp. 1711–1723.
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Ryazantseva, I.P. First-order regularization methods for accretive inclusions in a Banach space. Comput. Math. and Math. Phys. 54, 1647–1658 (2014). https://doi.org/10.1134/S0965542514110116
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DOI: https://doi.org/10.1134/S0965542514110116