Dual characterizations of relative continuity of convex functions
نویسندگان
چکیده
منابع مشابه
Characterizations of $L$-convex spaces
In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...
متن کاملCharacterizations of Convex Vector Functions and Optimization
In this paper we characterize nonsmooth convex vector functions by first and second order generalized derivatives. We also prove optimality conditions for convex vector problems involving nonsmooth data.
متن کاملGeometrically Relative Convex Functions
Abstract: In this paper, some new concepts of geometrically relative convex sets and relative convex functions are defined. These new classes of geometrically relative convex functions unify several known and new classes of relative convex functions such as exponential convex functions. New Hermite-Hadamard type integral inequalities are derived for these new classes of geometrically relative c...
متن کاملDual Characterizations of Set Containments with Strict Convex Inequalities
Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a nite union of convex sets (i.e. the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated systems. The conv...
متن کاملSecond-order Characterizations of Convex and Pseudoconvex Functions
The present paper gives characterizations of radially u.s.c. convex and pseudoconvex functions f : X → R defined on a convex subset X of a real linear space E in terms of first and second-order upper Dini-directional derivatives. Observing that the property f radially u.s.c. does not require a topological structure of E, we draw the possibility to state our results for arbitrary real linear spa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2001
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700002615