Multivalued Usco Functions and Stegall Spaces

  • Diana Ximena Narváez Universidad del Valle
Palabras clave: Bornology, usco mapping, subdifferential, Asplund spaces, Stegall spaces


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.


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Artículos de Investigación - Matemática