A STRONG CONVERGENCE AND NUMERICAL ILLUSTRATION FOR THE ITERATIVE METHODS TO SOLVE A SPLIT COMMON NULL POINT PROBLEM AND A VARIATIONAL INEQUALITY IN HILBERT SPACES

Nguyễn Thị Dinh; Phạm Thanh Hiếu

doi:10.34238/tnu-jst.4619

A STRONG CONVERGENCE AND NUMERICAL ILLUSTRATION FOR THE ITERATIVE METHODS TO SOLVE A SPLIT COMMON NULL POINT PROBLEM AND A VARIATIONAL INEQUALITY IN HILBERT SPACES

About this article

Received: 09/06/21 Revised: 05/11/21 Published: 05/11/21

Authors

1. Nguyen Thi Dinh , Hanoi University of Science and Technology
2. Pham Thanh Hieu, TNU - University of Agriculture and Forestry

Abstract

In this paper, we introduce two iterative methods to approximate the so lution of a split common null point problem and a variational inequality problem in Hilbert spaces. These problems have many important applica tions in the fields of signal processing, image processing, optimal control
and many other mathematical problems as well as real word situations. The considered methods are generated based on the Halpern method and the viscocity one which have been applied for many other problems such as the fixed point problem and the variational inequality. The strong conver gence of the method is proven with some certain conditions imposed on the parameters. Finally, a numerical example for solving an optimization problem in Euclidean spaces is given to illustrate the strong convergence of the proposed methods.

Keywords

Split feasibility problem; Null point problem; Variational inequality; Hillbert spaces; Nonexpansive mapping

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DOI: https://doi.org/10.34238/tnu-jst.4619

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