Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 27 (2020), No. 3, 1033--1049
Copyright Heldermann Verlag 2020

Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space

Mohammed Bachir
Laboratoire SAMM 4543, Université Panth\'eon-Sorbonne, 75634 Paris 13, France

We prove that any problem of minimization of proper lower semicontinuous function defined on a normal Hausdorff space is canonically equivalent to a problem of minimization of a proper weak-star lower semicontinuous convex function defined on a weak-star convex compact subset of some dual Banach space. We establish the existence of a bijective operator between the two classes of functions which preserves problems of minimization.

Keywords: Isomorphism, minimization problem, convex functions, normal Hausdorff space, the Stone-Cech compactification.

MSC: 47N10, 46N10, 46E15.

[ Fulltext-pdf  (148  KB)] for subscribers only.