A C1 function which is nowhere strongly paraconvex and nowhere semiconcave
O třináctém Hilbertově problému
Obecná teorie derivování funkcí a měr na katedře matematické analýzy MFF UK
A Lipschitz function which is on a.e. line need not be generically differentiable
We construct a Lipschitz function f on X = ℝ ² such that, for each 0 ≠ v ∈ X, the function f is smooth on a.e. line parallel to v and f is Gâteaux non-differentiable at all points of X except a first category set. Consequently, the same holds if X (with dimX > 1) is an arbitrary Banach space and “a.e.” has any usual “measure sense”. This example gives an answer to a natural question concerning the author’s recent study of linearly essentially smooth functions (which generalize essentially smooth...
ISTAM 87 - Bělehrad
On the intersection of the sets of the right and left internal approximate derivatives
Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space
On differentiation of metric projections in finite dimensional Banach spaces
On the differentiation of convex functions in finite and infinite dimensional spaces
Cluster sets of arbitrary functions in Euclidean spaces (Preliminary communication)
On the points of multiplicity of monotone operators
On approximate Dini derivates and one-sided approximate derivatives of arbitrary functions
On the points of multivaluedness of metric projections in separable Banach spaces
On the symmetry of Dini derivates of arbitrary functions
A note on partial derivatives of convex functions
Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces
Fréchet differentiability, strict differentiability and subdifferentiability
Porosity, derived numbers and knot points of typical continuous functions
An elementary proof of the one-dimensional Rademacher theorem
An elementary short proof of the one-dimensional Rademacher theorem on differentiability of Lipschitz functions is given.
On Lipschitz and d.c. surfaces of finite codimension in a Banach space
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated -ideals are studied. These -ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.
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