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A characterization of \(C^{1,1}\) functions via lower directional derivatives. (English) Zbl 1212.49043

Summary: The notion of \(\tilde {\ell }\)-stability is defined using the lower Dini directional derivatives and was introduced by the authors in their previous papers. In this paper we prove that the class of \(\tilde {\ell }\)-stable functions coincides with the class of \(C^{1,1}\) functions.

MSC:

49K40 Sensitivity, stability, well-posedness
26B05 Continuity and differentiation questions
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