Generalized Relaxed Quasimonotone Variational Inequality And Equilibrium Problem

In this dissertation, we introduce the broader class of multivalued generalized relaxed quasimonotone mappings in normed space. At first, using the KKM technique, we establish the existence of solutions of variational inequalities for such operators. Furthermore, we have proposed the relationship between the generalized quasiconvex function and the generalized relaxed quasimonotone mappings. At last, we use the generalized relaxed upper sign property to handle the Minty equilibrium problem. Consequently, we establish sufficient conditions for the existence of solutions of the equilibrium problem.