On strongly E-convex sets and strongly E-convex cone sets

Abstract EN

convex sets and -convex functions, which are considered as an important class of generalized convex sets and convex functions, have been introduced and studied by Youness [5] and other researchers.

This class has recently extended, by Youness, to strongly -convex sets and strongly -convex functions.

In these generalized classes, the definitions of the classical convex sets and convex functions are relaxed and introduced with respect to a mapping .

In this paper, new properties of strongly -convex sets are presented.

We define strongly -convex hull, strongly -convex cone, and strongly -convex cone hull and we proof some of their properties.

Some examples to illustrate the aforementioned concepts and to clarify the relationships between them are established