Open AccessOn strongly E-convex sets and strongly E-convex cone sets
Author(s) -
Saba Naser Majeed
Publication year - 2019
Publication title -
magallaẗ al-qādisiyyaẗ li-ʿulūm al-ḥāsibāt wa-al-riyāḍiyyāt
Language(s) - English
Resource type - Journals
eISSN - 2521-3504
pISSN - 2074-0204
DOI - 10.29304/jqcm.2019.11.1.459
Subject(s) - convex hull , subderivative , convex analysis , convex set , proper convex function , convex combination , mathematics , convex polytope , conic optimization , dual cone and polar cone , combinatorics , regular polygon , convex optimization , pure mathematics , geometry
-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.