NEW SUFFICIENT CONDITIONS FOR B-PREINVEXITY AND SOME EXTENSIONS
Vasile Preda, Diana-Elena Stanciu · 2011
The convexity and generalized convexity are very important in optimization. See for example [1–11, 15–17] and their references. Thus, the convexity was generalized to quasiconvexity, pseudoconvexity [11], invexity [5,7], F-convexity [14], ( ) , F ρ -convexity [15], B-vexity [1], preinvexity [8,17], B-preinvexity [16], and so on. In the following we consider the case of locally Lipschitz functions of B-preinvexity type [10,4,12,13]. Thus, we give some general sufficient conditions for B-preinvexity and properties and results for a new class introduced in this paper, the class of locally Lipschitz ( ) , , B d ρ -preinvex functions. We extend many results of B-vexity type stated in literature, for example [1,2,9,10,16] and their references.