On Borel Classes of Sets of Fréchet Subdifferentiability
We study possible Borel classes of sets of Fréchet subdifferentiability of continuous functions on reflexive spaces.
On continuity and monotonicity of Darboux functions
On continuous interval functions
On Denjoy property and on approximate partial derivatives
On differentiability of Peano type functions
On differentiability of Peano type functions
On differentiability of Peano type functions. II
On essential cluster sets
On full derivatives
On functions satisfying a local Lipschitz condition of order α
On -differentiability and difference properties of functions
On ordinary differentiability of Bessel potentials
On points of absolute continuity. Functions of several variables
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 some conditions which imply the continuity of almost all sections
Let be an open interval, a topological space and a metric space. Some local conditions implying continuity and quasicontinuity of almost all sections of a function are shown.
On some representations of almost everywhere continuous functions on
It is proved that the following conditions are equivalent: (a) f is an almost everywhere continuous function on ; (b) f = g + h, where g,h are strongly quasicontinuous on ; (c) f = c + gh, where c ∈ ℝ and g,h are strongly quasicontinuous on .
On symmetric partial derivatives an symmetric differentiability.
On the analytic approximation of differentiable functions from above
We determine conditions in order that a differentiable function be approximable from above by analytic functions, being left invariate on a fixed analytic subset which is a locally complete intersection.
On the characterization of quasiarithmetic means with weight function.