Geodesic
Newton--Kantorovich iterative regularization and generalized discrepancy principle for nonlinear ill-posed equations involving accretive mappings
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 38-44

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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. 
@article{IVM_2015_5_a3,
     author = {Nguyen Buong and Nguyen Duong Nguyen and Nguyen Thi Thu Thuy},
     title = {Newton--Kantorovich iterative regularization and generalized discrepancy principle for nonlinear ill-posed equations involving accretive mappings},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {38--44},
     publisher = {mathdoc},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_5_a3/}
}
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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. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 38-44. http://geodesic.mathdoc.fr/item/IVM_2015_5_a3/