Existence of solutions for nonlinear inequalities in G-convex spaces

By using a fixed-point theorem in G-convex spaces due to the first author, an existence result for abstract nonlinear inequalities without any monotonicity assumptions is established. As a consequence of our result, we obtain some further generalizations of recent known results. As application, an existence theorem for perturbed saddle point problems is obtained in noncompact G-convex spaces.