A theoretical view of existence results by using fixed point theory for quasi-variational inequalities

Abstract

In this paper, we present new existence results for the quasi-variational inequality problem (QV I) in reflexive Banach spaces using the fixed point method with quasi-monotonicity and local upper sign-continuity assumptions. These results improve upon previous ones which only required a weaker monotonicity condition and did not impose compactness on the involved set.

Keywords

• quasi-variational inequality
• fixed point
• quasi-monotonicity
• local upper sign-continuity