Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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REGULARIZATION FOR THE PROBLEM OF FINDING A SOLUTION OF A SYSTEM OF NONLINEAR MONOTONE ILL-POSED EQUATIONS IN BANACH SPACES

  • Tran, Thi Huong (College of Economics and Technology Thainguyen University) ;
  • Kim, Jong Kyu (Department of Mathematics Education Kyungnam University) ;
  • Nguyen, Thi Thu Thuy (Department of Mathematics College of Sciences Thainguyen University)
  • Received : 2017.07.25
  • Accepted : 2018.02.21
  • Published : 2018.07.01
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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.

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References

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