# Article

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Keywords:
second-order derivative; $C^{1,1}$ function; $\ell$-stable function; $\tilde {\ell }$-stability
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. This also solves the question posed by the authors in SIAM J. Control Optim. 45 (1) (2006), pp.\ 383--387.
References:
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