Multivalued Usco Functions and Stegall Spaces

  • Patricia Dávila


In this article we consider the study of the -differentiability and -ifferentiability for convex functions, not only in the general context of topological vector spaces (), but also in the context of Banach spaces. We study a special class of Banach spaces named Stegall spaces, denoted by , which is located between the Asplund -spaces and Asplund -spaces (-Asplund). We present a self-contained proof of the Stegall theorem, without appealing to the huge number of references required in some proofs available in the classical literature (4). This requires a thorough study of a very special type of multivalued functions between Banach spaces known as usco multi-functions.


Como citar
DÁVILA, Patricia. Multivalued Usco Functions and Stegall Spaces. Revista de Ciencias, [S.l.], v. 22, n. 1, oct. 2018. ISSN 2248-4000. Disponible en: <>. Fecha de acceso: 21 feb. 2019 doi:
Artículos de Investigación - Matemática

Palabras clave

Bornology, usco mapping, subdifferential, Asplund spaces, Stegall spaces