On relations of coefficient conditions.
On representation formulars for intermediate derivates.
On representations of Baire functions in a given family as sums of Baire Darboux functions with a common summand
On representations of some Perron integrable functions
On results of Jan Mařík in the theory of derivatives
Results of Jan Marik on the theory of derivatives of real functions are described.
On reverse Hardy's inequality.
On reverses of some inequalities in -inner product spaces.
On Riemann-Liouville and Caputo derivatives.
On Riemann-type definition for the wide Denjoy integral
On rings of Darboux functions
On rules of derivation with complex order for analytic and branched functions
On Schur convexity of some symmetric functions.
On sectorial qualitative cluster sets and directional qualitative cluster sets
On selections of multifunctions
The purpose of this paper is to introduce a definition of cliquishness for multifunctions and to study the search for cliquish, quasi-continuous and Baire measurable selections of compact valued multifunctions. A correction as well as a generalization of the results of [5] are given.
On semiconvexity properties of rotationally invariant functions in two dimensions
Let be a function defined on the set of all by matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function can be represented as a function of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of in terms of its representation
On sequences of real functions with the Darboux property
On sets of discontinuities of functions continuous on all lines
Answering a question asked by K. C. Ciesielski and T. Glatzer in 2013, we construct a -smooth function on and a closed set nowhere dense in such that there does not exist any linearly continuous function on (i.e., function continuous on all lines) which is discontinuous at each point of . We substantially use a recent full characterization of sets of discontinuity points of linearly continuous functions on proved by T. Banakh and O. Maslyuchenko in 2020. As an easy consequence of our...
On sets of non-differentiability of Lipschitz and convex functions
We observe that each set from the system (or even ) is -null; consequently, the version of Rademacher’s theorem (on Gâteaux differentiability of Lipschitz functions on separable Banach spaces) proved by D. Preiss and the author is stronger than that proved by D. Preiss and J. Lindenstrauss. Further, we show that the set of non-differentiability points of a convex function on is -strongly lower porous. A discussion concerning sets of Fréchet non-differentiability points of continuous convex...
On sets of points of semicontinuity in fine topologies generated by an ideal
On several new inequalities close to Hilbert-Pachpatte's inequality.