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Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

Jules, Florence, Lassonde, Marc (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak* Lipschitz...

Differentiation in Normed Spaces

Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

In this article we formalized the Fréchet differentiation. It is defined as a generalization of the differentiation of a real-valued function of a single real variable to more general functions whose domain and range are subsets of normed spaces [14].

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