On the symmetry of Dini derivates of arbitrary functions
On the transformers of derivatives
On the transformers of the Zahorski classes of functions
On the -finiteness of a variational measure
The -finiteness of a variational measure, generated by a real valued function, is proved whenever it is -finite on all Borel sets that are negligible with respect to a -finite variational measure generated by a continuous function.
On topological properties of the spaces of Darboux Baire 1 functions and bounded derivatives
We investigate the topological structure of the space 𝓓ℬ₁ of bounded Darboux Baire 1 functions on [0,1] with the metric of uniform convergence and with the p*-topology. We also investigate some properties of the set Δ of bounded derivatives.
On two mean value properties and functional equations associated with them.
On uniform symmetric derivatives
On Whitney pairs
A simple arc ϕ is said to be a Whitney arc if there exists a non-constant function f such that for every . G. Petruska raised the question whether there exists a simple arc ϕ for which every subarc is a Whitney arc, but for which there is no parametrization satisfying . We answer this question partially, and study the structural properties of possible monotone, strictly monotone and VBG* functions f and associated Whitney arcs.
Parametric differentiation
Path differentiation: further unification
A. M. Bruckner, R. J. O'Malley, and B. S. Thomson introduced path differentiation as a vehicle for unifying the theory of numerous types of generalized differentiation of real valued functions of a real variable. Part of their classification scheme was based on intersection properties of the underlying path systems. Here, additional light is shed on the relationships between these various types of path differentiation and it is shown how composite differentiation and first return differentiation...
Porosity, derived numbers and knot points of typical continuous functions
Positive derivatives and increasing functions.
Poznámka k článku V. Petrůva
Poznámka k jednomu problému K. Kartáka
Problèmes d'optimisation dépendant d'un paramètre à valeurs dans un espace de Banach
Problèmes variationnels et théorie du potentiel non linéaire
Pseudo-symmetric differentiation
Quasilineary Properties of Differentiable Functions in a Field with a Non-Archimedean Valuation.
Racines de fonctions différentiables
Nous précisons la classe de différentiabilité de où désigne une fonction positive de classe , -plate sur l’ensemble de ses zéros, et un réel, ; de plus, nous étudions l’existence locale d’une racine -ième de classe , pour une fonction de classe admettant une racine -ième formelle en chaque point.
Relations between some general nth-order derivatives