6 papers
Metric derived numbers and continuous metric differentiability via homeomorphisms
Jakub Duda, Olga Maleva
We define the notions of unilateral metric derivatives and ``metric derived numbers'' in analogy with Dini derivatives (also referred to as ``derived numbers'') and establish their…
Absolutely continuous functions with values in metric spaces
Jakub Duda
We present a general theory of absolutely continuous paths with values in metric spaces using the notion of metric derivatives. Among other results, we prove analogues of the Banac…
Generalized -variation and Lebesgue equivalence to differentiable functions
Jakub Duda
We find an equivalent condition for a real function to be Lebesgue equivalent to an -times differentiable function (); a simple solution in the case $n=2…
On Gateaux differentiability of pointwise Lipschitz mappings
Jakub Duda
We prove that for every function , where is a separable Banach space and is a Banach space with RNP, there exists a set $A\in\tilde\mcA$ such that is Gateaux…
Second order differentiability of paths via a generalized 1/2-variation
Jakub Duda
We find an equivalent condition for a continuous vector-valued path to be Lebesgue equivalent to a twice differentiable function. For that purpose, we introduce the notion of a $VB…
Cone monotone mappings: continuity and differentiability
Jakub Duda
We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces. We define two classes of monotone mappings bet…