Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities

This paper attempts to generalize and unify several new results that have been obtained in the ongoing research area of existence of solutions for equilibrium problems. First, we propose sufficient conditions, which include generalized monotonicity and weak coercivity conditions, for existence of equilibrium points. As consequences, we generalize various recent theorems on the existence of such solutions. For applications, we treat some generalized variational inequalities and complementarity problems. In addition, considering penalty functions, we study the position of a selected solution by relying on the viscosity principle.