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

• Accepted : 2018.02.21
• Published : 2018.07.01
• 31 4

#### 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;$Fr{\acute{e}}chet$ differentiable;Browder-Tikhonov regularization

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#### Acknowledgement

Supported by : National Research Foundation(NRF)