A class of complementarity problem and three classes of variational inequalities in real Banach spaces are introduced, and the equivalence among them are established under certain conditions. Several coercivity conditions are introduced for the existence of solutions of the generalized complementarity problem. Our results can be viewed as extension and generalization of the recent paper [N.-J. Huang, J. Li and D. O’Regan, Nonlinear Anal., Theory Methods Appl. 68, No. 12 (A), 3828–3840 (2008; Zbl 1191.90082)].