A Classical Olivier’s Theorem and Statistical Convergence

Šalát, Tibor, and Toma, Vladimír. "A Classical Olivier’s Theorem and Statistical Convergence." Annales mathématiques Blaise Pascal 10.2 (2003): 305-313. <http://eudml.org/doc/10492>.

@article{Šalát2003,
abstract = {L. Olivier proved in 1827 the classical result about the speed of convergence to zero of the terms of a convergent series with positive and decreasing terms. We prove that this result remains true if we omit the monotonicity of the terms of the series when the limit operation is replaced by the statistical limit, or some generalizations of this concept.},
affiliation = {Comenius University Department of Mathematics Mlynská dolina 84248 Bratislava SLOVAK REPUBLIC; Comenius University Department of Mathematics Mlynská dolina 84248 Bratislava SLOVAK REPUBLIC},
author = {Šalát, Tibor, Toma, Vladimír},
journal = {Annales mathématiques Blaise Pascal},
keywords = {classical Olivier's theorem; statistical convergence; statistical limit; monotonicity condition},
language = {eng},
month = {7},
number = {2},
pages = {305-313},
publisher = {Annales mathématiques Blaise Pascal},
title = {A Classical Olivier’s Theorem and Statistical Convergence},
url = {http://eudml.org/doc/10492},
volume = {10},
year = {2003},
}

TY - JOUR
AU - Šalát, Tibor
AU - Toma, Vladimír
TI - A Classical Olivier’s Theorem and Statistical Convergence
JO - Annales mathématiques Blaise Pascal
DA - 2003/7//
PB - Annales mathématiques Blaise Pascal
VL - 10
IS - 2
SP - 305
EP - 313
AB - L. Olivier proved in 1827 the classical result about the speed of convergence to zero of the terms of a convergent series with positive and decreasing terms. We prove that this result remains true if we omit the monotonicity of the terms of the series when the limit operation is replaced by the statistical limit, or some generalizations of this concept.
LA - eng
KW - classical Olivier's theorem; statistical convergence; statistical limit; monotonicity condition
UR - http://eudml.org/doc/10492
ER -