## Abstract

Given an ideal I on the positive integers, a real sequence (x_{n}) is said to be I-statistically convergent to ℓ provided that n∈N:[Formula presented]|{k≤n:x_{k}∉U}|≥ε∈Ifor all neighborhoods U of ℓ and all ε>0. First, we show that I-statistical convergence coincides with J-convergence, for some unique ideal J=J(I). In addition, J is Borel [analytic, coanalytic, respectively] whenever I is Borel [analytic, coanalytic, resp.]. Then we prove, among others, that if I is the summable ideal {A⊆N:∑_{a∈A}1∕a<∞} or the density zero ideal {A⊆N:lim_{n→∞}[Formula presented]|A∩[1,n]|=0} then I-statistical convergence coincides with statistical convergence. This can be seen as a Tauberian theorem which extends a classical theorem of Fridy. Lastly, we show that this is never the case if I is maximal.

Original language | English |
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Pages (from-to) | 83-95 |

Number of pages | 13 |

Journal | Indagationes Mathematicae |

Volume | 31 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2020 |

## Keywords

- Generalized density ideal
- Ideal statistical convergence
- Maximal ideals
- Submeasures
- Tauberian condition

## ASJC Scopus subject areas

- Mathematics(all)