System of split variational inequality problems

TL;DR

This paper introduces a new iterative algorithm for solving systems of split variational inequality problems in Hilbert spaces, proving strong convergence and extending previous results in the field.

Contribution

It proposes a novel projection-based iterative method for systems of split variational inequalities, generalizing and improving existing approaches.

Findings

The algorithm converges strongly to a solution.

The method unifies and extends prior results.

It broadens the applicability of variational inequality solutions.

Abstract

In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that the sequence generated by the iterative algorithm converges strongly to a solution of the system of split variational inequality problems. Furthermore, we discuss some consequences of the main result. The iterative algorithms and results presented in this paper generalize, unify and improve the previously known results of this area.