CONTINUOUS REGULARIZATION METHOD FOR A COMMON MINIMUM POINT OF A FINITE SYSTEM OF CONVEX FUNCTIONALS

Abstract

The concept of the ill-posed problem was introduced by Hadamard, a French mathematician in 1932 when he studied the effect of the boundary value problem on differential equations. Due to the unstability of the ill-posed problems, the numerical computation is difficult to do. Therefore, one of the main study directions for ill-posed problems is construct stable methods to solve this problems such that when the error of the input data is smaller, the approximate solution is closer to the correct solution of the original problem. Although there are some known important results obtained in studying the regularization method for solving the ill-posed problems, the improvement of the methods to increase their effectiveness always attracts the attention of many researchers. In this paper, we present a regularization method for a common minimum point of a finite system of Gateau differentiable weakly lower semi-continuous and properly convex functionals on real Hilbert spaces. And then, an application our theoretical results to convex feasibility problems and common fixed points of nonexpansive mappings.