Journal of Convex Analysis, Vol. 6, No. 2, pp. 387-393 (1999)

A Note on the Closedness of the Convex Hull and Its Applications

F. H\"{u}sseinov

Department of Economics, Bilkent University, 06533 Bilkent, Ankara, Turkey,

Abstract: This paper answers the following question motivated by the problem of spannability of functions. When is the convex hull of an unbounded (closed) set closed? We provide necessary and sufficient conditions for the closedness of the convex hull. Then we apply these results to the problem of spannability of functions playing an important role in mathematical economics and variational calculus. Resulting characterizations of spannability of functions imply previously known sufficiency conditions for spannability.

Classification (MSC2000): 52A20

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 1999--2000 ELibM for the EMIS Electronic Edition