Variational-Like Inequality Problems Involving Set-Valued Maps and Generalized Monotonicity

An Existence Result for a Variational-Like inequality

“…If η(x, y) = x − y the problem (1.1) becomes a classical generalised variational inequality. In many existing papers on variational-like problems, it is supposed that the function η is affine in the first variable [6,15] or that the mapping y → z * , η(y, x) is convex [3]. In this paper we obtain an existence result in the case where η satisfies a weaker assumption.…”

“…They generalised the classical variational inequalities by replacing the difference y − x that appears in their formulation by a more general function η(y, x). Subsequently, many authors continued the research in infinitedimensional Banach spaces, for various extensions of the original problem (see, for instance, [3,4,6,14,15] and the references therein). A related class of problems, called general variational inequalities, was introduced and studied by Noor [12].…”