J. Duda

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math.CA2006

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…

math.CA2005

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…

math.CA2005

Generalized $α$ -variation and Lebesgue equivalence to differentiable functions

Jakub Duda

We find an equivalent condition for a real function $f : [a, b] \to R$ to be Lebesgue equivalent to an $n$ -times differentiable function ( $n \geq 2$ ); a simple solution in the case $n=2…

math.CA2005

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…

Metric derived numbers and continuous metric differentiability via homeomorphisms

Absolutely continuous functions with values in metric spaces

Generalized α-variation and Lebesgue equivalence to differentiable functions

Second order differentiability of paths via a generalized 1/2-variation

Generalized $α$ -variation and Lebesgue equivalence to differentiable functions