Quasi-equilibrium problems with generalized monotonicity

Abstract

In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of solution sets of equilibrium problems and convex feasibility problems. Moreover, we show that the concept of pseudomonotonicity and upper sign property are related under suitable assumptions.