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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 5, Pages 38–44
(Mi ivm8997)
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Newton–Kantorovich iterative regularization and generalized discrepancy principle for nonlinear ill-posed equations involving accretive mappings
Nguyen Buonga, Nguyen Duong Nguyenb, Nguyen Thi Thu Thuyc a Vietnamese Academy of Science and Technology, Institute of Information Technology, 18, Hoang Quoc Viet, Hanoi, Vietnam
b Vietnamese Foreign Trade University, Hanoi, Vietnam
c Thainguyen College of Sciences, Thainguyen University, Vietnam
Abstract:
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.
Keywords:
accretive and $\alpha$-strong accretive mapping, reflexive Banach space, Fréchet differentiable and the Browder–Tikhonov regularization.
Received: 23.11.2013
Citation:
Nguyen Buong, Nguyen Duong Nguyen, Nguyen Thi Thu Thuy, “Newton–Kantorovich iterative regularization and generalized discrepancy principle for nonlinear ill-posed equations involving accretive mappings”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 5, 38–44; Russian Math. (Iz. VUZ), 59:5 (2015), 32–37
Linking options:
https://www.mathnet.ru/eng/ivm8997 https://www.mathnet.ru/eng/ivm/y2015/i5/p38
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