Abstract

NARVAEZ, Diana Ximena. Multivalued Usco Functions and Stegall Spaces. rev. cienc. [online]. 2018, vol.22, n.1, pp.45-71. ISSN 0121-1935.  https://doi.org/10.25100/rc.v22i1.7100.

In this article we consider the study of the 𝐺 -differentiability and F-ifferentiability for convex functions, not only in the general context of topological vector spaces (𝑡. 𝑣. 𝑠.), but also in the context of Banach spaces. We study a special class of Banach spaces named Stegall spaces, denoted by 𝕾, which is located between the Asplund 𝐹-spaces and Asplund 𝐺-spaces (𝒢-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 (1). This requires a thorough study of a very special type of multivalued functions between Banach spaces known as usco multi-functions.

Keywords : Bornology; usco mapping; subdifferential; Asplund spaces; Stegall spaces.

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