What question did this study set out to answer?

The aim is to establish a theorem for finding solutions to variational inequality problems using specific mappings.

March 28, 2026

Solution of variational inequality problems using monotone mapping

APAnju PanwarMaharshi Dayanand University PKPradeep KumarMaharshi Dayanand University RMReena MorwalGovernment of Haryana

Key Points

The aim is to establish a theorem for finding solutions to variational inequality problems using specific mappings.
Proved a weak convergence theorem.
Applied the theorem to monotone and Lipschitz continuous mappings.
Focused on problems within Hilbert space.
Demonstrated convergence for the proposed mapping.
Showed applicability to constrained convex optimization problems.
Indicated effectiveness in solving split feasibility problems.

Abstract

Abstract In this paper, a weak convergence theorem is proved to find out the solution of variational inequality problem for a mapping which is monotone as well as Lipschitz continuous in Hilbert space. This result can also be used to determine the solutions of constrained convex optimization and split feasibility problems.

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