Newton--Kantorovich iterative regularization and generalized discrepancy principle for nonlinear ill-posed equations involving accretive mappings

Nguyen Buong ; Nguyen Duong Nguyen ; Nguyen Thi Thu Thuy

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 38-44.

Résumé

In this paper, in order to solve nonlinear ill-posed operator equations involving an $m$-accretive mapping on a real Banach space, that does not admit a weak sequential continuous duality mapping, we prove a strongly convergent theorem for Newton–Kantorovich iterative regularization method with a posteriori stopping rule. In our results, the Lipschitz continuity of the derivatives for the mapping is overcomed.

Détail

Keywords: accretive and $\alpha$-strong accretive mapping, reflexive Banach space, Fréchet differentiable and the Browder–Tikhonov regularization.

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