25 citations · 46 across the 18 of their papers we have counts for
11 papers · 1 filter
The Fréchet derivative is in the first Baire class
Eva Kopecká, Luděk Zaj\'ıček
Let be a normed linear space, a Banach space, an open set and a mapping. We show that the Fréchet derivative of is of the first Baire clas…
On Whitney extension theorem in Banach spaces
Michal Johanis, Luděk Zajíček
Our note is a complement to recent articles \cite{JS1} (2011) and \cite{JS2} (2013) by M. Jiménez-Sevilla and L. Sánchez-González which generalise (the basic statement of) the clas…
Frechet differentiability via partial Frechet differentiability
Ludek Zajicek
Let be Banach spaces and a real function on . Let be the set of all points at which is partially Fr\' echet…
On sets of discontinuities of functions continuous on all lines
Ludek Zajicek
Answering a question asked by K.C. Ciesielski and T. Glatzer in 2013, we construct a -smooth function on and a set nowhere dense…
On the set of points at which an increasing continuous singular function has a nonzero finite derivative
Marta Kossaczka, Ludek Zajicek
Sanchez, Viader, Paradis and Carrillo (2016) proved that there exists an increasing continuous singular function on such that the set of points where has a no…
Properties of Hadamard directional derivatives: Denjoy-Young-Saks theorem for functions on Banach spaces
Ludek Zajicek
The classical Denjoy-Young-Saks theorem on Dini derivatives of arbitrary functions was extended by U.S. Haslam-Jones (1932) and A.J. Ward (1935) to arbitrary functio…
G\^ ateaux and Hadamard differentiability via directional differentiability
Ludek Zajicek
Let be a separable Banach space, a Banach space and an arbitrary mapping. Then the following implication holds at each point except a -directional…
Hadamard differentiability via G\^ ateaux differentiability
Ludek Zajicek
Let be a separable Banach space, a Banach space and a mapping. We prove that there exists a -directionally porous set such that if $x\in X \set…
On extensions of d.c. functions and convex functions
Libor Vesely, Ludek Zajicek
We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natura…
Quotients of continuous convex functions on nonreflexive Banach spaces
P. Holicky, O. Kalenda, L. Vesely +1
On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions…
On Lipschitz and d.c. surfaces of finite codimension in a Banach space
Luděk Zajíček
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space, and properties of generated -ideals are studied. These -ideals naturally appear in the diff…