System of split variational inequality problems in semi-inner product spaces

TL;DR

This paper introduces a new system of split variational inequality problems in semi-inner product spaces, proposing an iterative algorithm with convergence analysis, extending previous models and providing special case discussions.

Contribution

It extends split variational inequality problems to semi-inner product spaces and develops an iterative solution method with convergence proof.

Findings

Proposed an iterative algorithm for the new problem system.

Proved convergence of the algorithm under certain conditions.

Discussed special cases derived from the main results.

Abstract

We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for computing the approximate solution of the system of split variational inequality problems. Further, the convergence analysis of the iterative algorithm is also discussed. Several special cases which can be obtained from the main result are also discussed.