REGULARIZATION FOR THE PROBLEM OF FINDING A SOLUTION OF A SYSTEM OF NONLINEAR MONOTONE ILL-POSED EQUATIONS IN BANACH SPACES

• Published in: Journal of the Korean Mathematical Society Vol. 55; no. 4; pp. 849 - 875
• Main Authors: Tran, Thi Huong, Kim, Jong Kyu, Nguyen, Thi Thu Thuy
• Format: Journal Article
• Language: Korean
• Published: 2018
• Subjects: monotone mapping; Fr{\acute{e}}chet$ differentiable; Browder-Tikhonov regularization; strictly convex Banach space; hemicontinuous
• ISSN: 0304-9914

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.