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Subjects
49-XX Calculus of variations and optimal control; optimization
49Jxx Existence theories
49J50 Fréchet and Gateaux differentiability

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Remarks on delta-convex functions

Eva Kopecká, Jan Malý (1990)

Commentationes Mathematicae Universitatis Carolinae

Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions

Luděk Zajíček (2014)

Commentationes Mathematicae Universitatis Carolinae

We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on $Γ$ -almost everywhere Fréchet differentiability of Lipschitz functions on $c_{0}$ (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at $Γ$ -almost every $x$ at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are $Γ$ -almost everywhere Fréchet differentiable....

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