Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense
After a brief summary of Tauberian conditions for ordinary sequences of numbers, we consider summability of double sequences of real or complex numbers by weighted mean methods which are not necessarily products of related weighted mean methods in one variable. Our goal is to obtain Tauberian condit...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204403329 |
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| author | Ferenc Móricz U. Stadtmüller |
| author_facet | Ferenc Móricz U. Stadtmüller |
| author_sort | Ferenc Móricz |
| collection | DOAJ |
| description | After a brief summary of Tauberian conditions for
ordinary sequences of numbers, we consider summability of double
sequences of real or complex numbers by weighted mean methods
which are not necessarily products of related weighted mean
methods in one variable. Our goal is to obtain Tauberian
conditions under which convergence of a double sequence follows
from its summability, where convergence is understood in
Pringsheim's sense. In the case of double sequences of real numbers,
we present necessary and sufficient Tauberian conditions, which are so-called
one-sided conditions. Corollaries allow these Tauberian conditions
to be replaced by Schmidt-type slow decrease conditions.
For double sequences of complex numbers, we present necessary and
sufficient so-called two-sided Tauberian conditions.
In particular, these conditions are satisfied if the summable
double sequence is slowly oscillating. |
| format | Article |
| id | doaj-art-097c42916cc44f70a2ba21d21e13e336 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-097c42916cc44f70a2ba21d21e13e3362025-02-03T06:14:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004653499351110.1155/S0161171204403329Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's senseFerenc Móricz0U. Stadtmüller1Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged 6720, HungaryAbteilung Zahlentheorie und Wahrscheinlichkeitstheorie, Fakultät für Mathematik und Wirtschaftswissenschaften, Universität Ulm, Ulm 89069, GermanyAfter a brief summary of Tauberian conditions for ordinary sequences of numbers, we consider summability of double sequences of real or complex numbers by weighted mean methods which are not necessarily products of related weighted mean methods in one variable. Our goal is to obtain Tauberian conditions under which convergence of a double sequence follows from its summability, where convergence is understood in Pringsheim's sense. In the case of double sequences of real numbers, we present necessary and sufficient Tauberian conditions, which are so-called one-sided conditions. Corollaries allow these Tauberian conditions to be replaced by Schmidt-type slow decrease conditions. For double sequences of complex numbers, we present necessary and sufficient so-called two-sided Tauberian conditions. In particular, these conditions are satisfied if the summable double sequence is slowly oscillating.http://dx.doi.org/10.1155/S0161171204403329 |
| spellingShingle | Ferenc Móricz U. Stadtmüller Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense International Journal of Mathematics and Mathematical Sciences |
| title | Summability of double sequences by weighted mean methods and
Tauberian conditions for convergence in Pringsheim's sense |
| title_full | Summability of double sequences by weighted mean methods and
Tauberian conditions for convergence in Pringsheim's sense |
| title_fullStr | Summability of double sequences by weighted mean methods and
Tauberian conditions for convergence in Pringsheim's sense |
| title_full_unstemmed | Summability of double sequences by weighted mean methods and
Tauberian conditions for convergence in Pringsheim's sense |
| title_short | Summability of double sequences by weighted mean methods and
Tauberian conditions for convergence in Pringsheim's sense |
| title_sort | summability of double sequences by weighted mean methods and tauberian conditions for convergence in pringsheim s sense |
| url | http://dx.doi.org/10.1155/S0161171204403329 |
| work_keys_str_mv | AT ferencmoricz summabilityofdoublesequencesbyweightedmeanmethodsandtauberianconditionsforconvergenceinpringsheimssense AT ustadtmuller summabilityofdoublesequencesbyweightedmeanmethodsandtauberianconditionsforconvergenceinpringsheimssense |