**MSC2010** 65J15

### Сontinuous regularization analog of Newton method for m-accretive equations

#### I. P. Ryazantseva^{1}

Annotation | In Banach spaces for nonlinear equations corresponding to the approximate setting data( the operator and the right part of a given operator equation) with the Frechet differentiable on m-accretive operator constructed a regularized continuous analog of Newton's method obtained sufficient conditions for its strong convergence to a certain solution of the given equation determined uniquely. Previously we prove auxiliary assertions of continuity of values that is determined through regularized solutions and their derivatives. The approximations of the operator are assumed to be differentiable. The unique solvability of the differential equation defining the investigated regularization method is proved. In the proof of convergence of the continuous method is known for the convergence of operator regularization method for accretive equations. Requirements on the geometry of Banach spaces and its conjugate are performed for a wide class of Banach spaces. For the approximate task right side of the equation separately studied the cases of the unperturbed and of the perturbed operator. Built examples of parametric functions that are used in the equation defining the study method. Is an example of an operator arising in the theory of a scalar density function, for which the conditions of convergence of the method are performed. |
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Keywords | Banach space, m-accretive operator, duality mapping, method of Newton, continuous method, perturbed data, regularization, convergence |

^{1}**Irina P. Ryazantseva**, Professor, Department of Applied Mathematics, Nizhny Novgorod State Tehnical University after R.E. Alekseev (24 Minina Str., Nizhny Novgorod 603950, Russia), Dr. Sci. (Phys.-Math.), ORCID: http://orcid.org/0000-0001-6215-1662, lryazantseva@applmath.ru

**Citation**: I. P. Ryazantseva, "[Сontinuous regularization analog of Newton method for m-accretive equations]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:1 (2017) 77–87 (In Russian)

**DOI** 10.15507/2079-6900.19.2017.01.77-87