J. Korean Math. Soc. 2018; 55(4): 849-875
Online first article March 15, 2018 Printed July 1, 2018
https://doi.org/10.4134/JKMS.j170494
Copyright © The Korean Mathematical Society.
Tran Thi Huong, Jong Kyu Kim, Nguyen Thi Thu Thuy
Thainguyen University, Kyungnam University, Thainguyen University
The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and $N$ inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.
Keywords: monotone mapping, hemicontinuous, strictly convex Banach space, Fr\'echet differentiable, Browder--Tikhonov regularization
MSC numbers: 47H17, 47H20
2011; 48(3): 641-653
2012; 49(1): 187-200
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