Tauberian Theorems for Sequences in 2-Normed Spaces

被引：9

作者：

Savas, Rahmet ^{[1
]}

Sezer, Sefa Anil ^{[1
]}

机构：

[1] Istanbul Medeniyet Univ, Dept Math, Istanbul, Turkey

来源：

RESULTS IN MATHEMATICS | 2017年 / 72卷 / 04期

关键词：

Tauberian theorems; 2-normed spaces; slowly oscillating sequences; two-sided Tauberian conditions; STATISTICAL CONVERGENCE; CESARO SUMMABILITY; IDEAL CONVERGENCE;

D O I：

10.1007/s00025-017-0747-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we initiate the study of Tauberian theorems for sequences in 2-normed spaces. We introduce a necessary and sufficient Tauberian condition for (C, 1) summable sequences in such spaces. Corollaries allow this condition to be replaced by 2-normed analogues of Schmidt-type slow oscillation condition or Hardy-type two-sided condition.

引用

页码：1919 / 1931

页数：13

共 24 条

[1]

[Anonymous], 1897, MONATSH MATH

[2]

[Anonymous], 2002, Publ. Inst. Math. (Belgr.)

[3]

Belen C, 2015, HACET J MATH STAT, V44, P513

[4] Lacunary Ward Continuity in 2-normed Spaces [J].

Cakalli, Huseyin ;

Ersan, Sibel .

FILOMAT, 2015, 29 (10) :2257-2263

[5] Statistical Extensions of Some Classical Tauberian Theorems for Cesaro Summability of Triple Sequences [J].

Canak, Ibrahim ;

Onder, Zerrin ;

Totur, Umit .

RESULTS IN MATHEMATICS, 2016, 70 (3-4) :457-473

[6] Alternative proofs of some classical type Tauberian theorems for the Cesaro summability of integrals [J].

Canak, Ibrahim ;

Totur, Umit .

MATHEMATICAL AND COMPUTER MODELLING, 2012, 55 (3-4) :1558-1561

[7] TWO VALUED MEASURE AND SOME NEW DOUBLE SEQUENCE SPACES IN 2-NORMED SPACES [J].

Das, Pratulananda ;

Savas, Ekrem ;

Bhunia, Santanu .

CZECHOSLOVAK MATHEMATICAL JOURNAL, 2011, 61 (03) :809-825

[8]

Dik M., 2001, MATH MORAV, V5, P57, DOI DOI 10.5937/MATMOR0105057D

[9]

Dutta H, 2012, SOUTHEAST ASIAN BULL, V36, P197

[10]

Ghler S., 1964, Math. Nachr, V28, P1, DOI [DOI 10.1002/MANA.19640280102, 10.1002/mana.19640280102]

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