O jedné ze stěžejních otázek nauky o funkcích
Obecná teorie derivování funkcí a měr na katedře matematické analýzy MFF UK
Old Friends Revisited; the Multifunctional Nature of Some Classical Functions.
On approximate Dini derivates and one-sided approximate derivatives of arbitrary functions
On continuous functions and the approximate symmetric derivatives
On continuous functions with no unilateral derivatives
We construct a family of continuous functions on the unit interval which have nowhere a unilateral derivative finite or infinite by using De Rham’s functional equations. Then we show that for any
On convolution of continuous functions
On differentiability with respect to parameters of the Lebesgue integral.
On Kantorovich's result on the symmetry of Dini derivatives
For , let be the set of points at which is Lipschitz from the left but not from the right. L.V. Kantorovich (1932) proved that, if is continuous, then is a “()-reducible set”. The proofs of L. Zajíček (1981) and B.S. Thomson (1985) give that is a -strongly right porous set for an arbitrary . We discuss connections between these two results. The main motivation for the present note was the observation that Kantorovich’s result implies the existence of a -strongly right porous set ...
On some Marcus problem concerning functions possessing the derivative at points of discontinuity only
On the complexification of the Weierstrass non-differentiable function.
On the derivative of type α
On the differentiability of certain saltus functions
We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function f investigated in the past, f’(ξ) = 0 if f’(ξ) exists and is finite, we show how, for example, an increasing real function g can be constructed so that for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.
On the Differentiability of the Coordinate Functions of Póyla's Space-Filling Curve.
On the differentiation of convex functions
On the differentiation of convex functions in finite and infinite dimensional spaces
On the functional equation f(...(x) + g(y)) = ..(x) * h(x+y). (Short Communication).
On the functional equation f(...(x) + g(y)) = ...(x) * h(x+y).
On the number of minimal pairs of compact convex sets that are not translates of one another
Let [A,B] be the family of pairs of compact convex sets equivalent to (A,B). We prove that the cardinality of the set of minimal pairs in [A,B] that are not translates of one another is either 1 or greater than ℵ₀.
On the symmetric derivative