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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 4

Issues

Weighted uniform density ideals

Jacek Tryba
Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0139

Abstract

Weighted uniform densities are a generalization of the uniform density, which is also known as the Banach density. In this paper, we introduce the concept of weighted uniform density ideals and consider the topological complexity of these ideals as well as when they have certain analytical properties related to the ideal convergence of sequences and series. Furthermore, we prove some inequalities between different upper and lower weighted uniform densities and give the answer to the problem concerning the Darboux property of these densities.

MSC 2010: Primary 11B05; Secondary 40A35; 40A05

Keywords: uniform density; Banach density; weighted uniform density; Darboux property; ideal; filter; P-ideal; ideal convergence; 𝓘-convergent series

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About the article

Received: 2016-05-10

Accepted: 2017-06-06

Published Online: 2018-08-06

Published in Print: 2018-08-28


Communicated by Ján Borsík


Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 717–726, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0139.

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