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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.

Narváez, D. X. (2018). Multivalued Usco Functions and Stegall Spaces. Revista De Ciencias, 22(1). https://doi.org/10.25100/rc.v22i1.7100