Generalized variational inequalities for maximal monotone operators

TL;DR

This paper extends the theory of generalized variational inequalities for maximal monotone operators in infinite-dimensional Banach spaces, providing new existence results and insights into the structure of solution sets.

Contribution

It introduces new theorems on the existence and structure of solutions for generalized variational inequalities in reflexive Banach spaces, extending prior finite-dimensional results.

Findings

Established existence of solutions in reflexive Banach spaces

Characterized the structure of solution sets

Extended finite-dimensional results to infinite-dimensional spaces

Abstract

In this paper we present some new results on the existence of solutions of generalized variational inequalities in real reflexive Banach spaces with Fr\'echet differentiable norms. Moreover, we also give some theorems about the structure of solution sets. The results obtained in this paper improve and extend the ones announced by Fang and Peterson [1] to infinite dimensional spaces.