Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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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.

Regularization for the problem of finding a solution of a system of nonlinear monotone ill-posed equations in Banach spaces

Tran Thi Huong, Jong Kyu Kim, Nguyen Thi Thu Thuy

Thainguyen University, Kyungnam University, Thainguyen University

Abstract

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