### Abstract

Two classes of numerical sequences are defined by means certain properties of the differences of terms of positive sequences, and their relationship to some newly defined classes and the well-known Sidon-Telyakovskiǐ class is analyzed. It is also verified that if a sequence belongs to the newly defined wider class, then with this sequence in place of the sequence {1/k} an essential inequality established by Telyakovskiǐ can be generalized notably. This new result and the previous generalizations of the original Telyakovskiǐ's theorem are incomparable.

Original language | English |
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Pages (from-to) | 161-172 |

Number of pages | 12 |

Journal | Analysis Mathematica |

Volume | 37 |

Issue number | 3 |

DOIs | |

Publication status | Published - szept. 2011 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**A generalization of a basic inequality of Telyakovskiǐ.** / Leindler, L.

Research output: Article

*Analysis Mathematica*, vol. 37, no. 3, pp. 161-172. https://doi.org/10.1007/s10476-011-0301-y

}

TY - JOUR

T1 - A generalization of a basic inequality of Telyakovskiǐ

AU - Leindler, L.

PY - 2011/9

Y1 - 2011/9

N2 - Two classes of numerical sequences are defined by means certain properties of the differences of terms of positive sequences, and their relationship to some newly defined classes and the well-known Sidon-Telyakovskiǐ class is analyzed. It is also verified that if a sequence belongs to the newly defined wider class, then with this sequence in place of the sequence {1/k} an essential inequality established by Telyakovskiǐ can be generalized notably. This new result and the previous generalizations of the original Telyakovskiǐ's theorem are incomparable.

AB - Two classes of numerical sequences are defined by means certain properties of the differences of terms of positive sequences, and their relationship to some newly defined classes and the well-known Sidon-Telyakovskiǐ class is analyzed. It is also verified that if a sequence belongs to the newly defined wider class, then with this sequence in place of the sequence {1/k} an essential inequality established by Telyakovskiǐ can be generalized notably. This new result and the previous generalizations of the original Telyakovskiǐ's theorem are incomparable.

UR - http://www.scopus.com/inward/record.url?scp=80051610881&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051610881&partnerID=8YFLogxK

U2 - 10.1007/s10476-011-0301-y

DO - 10.1007/s10476-011-0301-y

M3 - Article

AN - SCOPUS:80051610881

VL - 37

SP - 161

EP - 172

JO - Analysis Mathematica

JF - Analysis Mathematica

SN - 0133-3852

IS - 3

ER -