1 citations · 1 across the 6 of their papers we have counts for
6 papers
On differentiation with respect to filters
Dmytro Seliutin
This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper…
On integration with respect to filter
Dmytro Seliutin
Using a concept of filter we propose one generalization of Riemann integral, that is integration with respect to filter. We study this problem, demonstrate different properties and…
On relation between statistical ideal and ideal generated by a modulus function
Dmytro Seliutin
We characterize those modulus functions for which the ideal generated by is equal to the statistical ideal.
Completeness in topological vector spaces and filters on N
Vladimir Kadets, Dmytro Seliutin
We study completeness of a topological vector space with respect to different filters on the set N of all naturals. In the metrizable case all these kinds of completeness are the s…
Conglomerated filters, statistical measures, and representations by ultrafilters
Vladimir Kadets, Dmytro Seliutin
Using a new concept of conglomerated filter we demonstrate in a purely combinatorial way that none of Erdös-Ulam filters or summable filters can be generated by a single statistica…
Carmichael numbers for
Eugene Karolinsky, Dmytro Seliutin
We propose a generalization of Carmichael numbers, where the multiplicative group is replaced by for . We prove ba…