GENERALISED α-m MONOTONICITY AND β-WELL POSEDNESS OF SET VARIATIONAL INEQUALITY PROBLEM

Abstract

This paper attempts to introduce two new concepts of monotonicty defined on semi-inner product spaces to analyse well-posedness for variational inequality problems. These concepts are generalised α-m monotonicity and generalised α-m pseudomonotonicity for set maps. We also present a new concept of well-posedness, namely β-well-posedness for set variational inequality problem (VI). We further study the relationship of these monotone maps along with (VI). Then we demonstrate a gap function
for the above (VI). Beneath the assumption of the said pseudo-monotonicity, a result is obtained showing the relation between the solution and gap function of the said (VI) problem. Finally, with the help of this gap function, we formulate said variational inequality problem into a corresponding mathematical programming problem (MP) and establish the relations between the β-well-posedness of both problems.