On Second-Order Generalized Convexity

Second-order convex functions were introduced by Mond (Opsearch 11(2–3):90–99, 1974) in order to deal with second-order duality. Then that notion was generalized again and again, using more and more parameters introduced using several quantifiers. In the present paper, we show that most of these notions have quite simple intrinsic characterizations. This paper can be viewed as a continuation of our paper (Zălinescu in An Ştiinţ Univ Al I Cuza Iaşi Secţ I a Mat 35(3):213–220, 1989) in which we characterized generalized bonvex functions.