Further Generalizations of Minimax Inequalities for Mixed Concave-Convex Functions and Applications

In this paper we obtain a minimax inequality for generalized mixed concave-convex functions which contain the corresponding results from the literature as special cases and improves the corresponding result in (B. L. Lin and X. C. Quan, J. Math. Anal. Appl.161 (1991), 587-590). As applications, in Sections 3 and 4, we utilize the results presented in this paper to study the abstract variational inequality problem and the coincidence point problem for set-valued mappings and for saddle problems.