Generalised Mixed Vector Equilibrium Problem with New Relaxed Monotonicity

Abstract

In this paper, we introduce a new notion of relaxed α—β— C monotonicity for bi-mappings. It has been shown that the α—β— C monotonicity is a proper generalisation of monotonicity. Using the KKM technique, we obtain the existence of solutions for generalised mixed vector equilibrium problem with relaxed α—β— C monotonicity in reflexive Banach spaces. Some examples are also given.