O prvních spojitých singulárních funkcích
Obecná teorie derivování funkcí a měr na katedře matematické analýzy MFF UK
Old Friends Revisited; the Multifunctional Nature of Some Classical Functions.
On classification of real singularities.
On connectivity points of Darboux functions
On Darboux selections
On Darboux solutions of the Euler's equation.
On Multiply Periodic Real Functions: An Addendum.
On Probability Distribution Solutions of a Functional Equation
Let 0 < β < α < 1 and let p ∈ (0,1). We consider the functional equation φ(x) = pφ (x-β)/(1-β) + (1-p)φ(minx/α, (x(α-β)+β(1-α))/α(1-β)) and its solutions in two classes of functions, namely ℐ = φ: ℝ → ℝ|φ is increasing, , , = φ: ℝ → ℝ|φ is continuous, , . We prove that the above equation has at most one solution in and that for some parameters α,β and p such a solution exists, and for some it does not. We also determine all solutions of the equation in ℐ and we show the exact connection...
On some new properties of the Cantor set
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 existence of functions with perfect level sets.
On the family of functions with a closure of its graph of measure zero
On the maximum of generalized Darboux functions