Abstract
The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces. Based on the KKM technique, the solvability of this kind of nonlinear variational inequalities is presented. The obtained results extend, improve, and unify the results due to Browder, Carbone, Siddiqi, Ansari, Kazmi, Verma, and others.
Highlights
It is well known that variational inequality theory has significant applications in various fields of mathematics, physics, economics, and engineering science
Siddiqi et al [6] considered the solvability of a class of nonlinear variational inequality problems in nonempty closed convex subsets and nonempty compact convex subsets of reflexive Banach spaces and locally convex spaces, respectively
Verma [7] presented the existence and uniqueness of solutions for a class of nonlinear variational inequality problems involving a combination of operators of p-monotone and p-Lipschitz types, which generalizes a result due to Browder [1]
Summary
It is well known that variational inequality theory has significant applications in various fields of mathematics, physics, economics, and engineering science. Siddiqi et al [6] considered the solvability of a class of nonlinear variational inequality problems in nonempty closed convex subsets and nonempty compact convex subsets of reflexive Banach spaces and locally convex spaces, respectively.
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