Split general quasi-variational inequality problem

TL;DR

This paper introduces a new split general quasi-variational inequality problem, extending existing inequality problems in Hilbert spaces, and proposes an iterative algorithm with convergence analysis.

Contribution

It defines a novel inequality problem and develops a unified iterative solution method with convergence criteria, generalizing prior results.

Findings

Proposed an iterative algorithm for the split general quasi-variational inequality problem.

Established convergence criteria for the proposed algorithm.

Unified and extended existing results in variational inequality problems.

Abstract

In this paper, we introduce a split general quasi-variational inequality problem which is a natural extension of split variational inequality problem, quasi-variational and variational inequality problems in Hilbert spaces. Using projection method, we propose an iterative algorithm for the split general quasi-variational inequality problem and discuss some its special cases. Further, we discuss the convergence criteria of these iterative algorithms. The results presented in this paper generalize, unify and improve the previously known many results for the quasi-variational and variational inequality problems.