A new theorem on boundedness and absolute summability

2018 ◽  
Author(s):  
Hikmet Seyhan Özarslan ◽  
Bağdagül Kartal
Keyword(s):  
Absolute Summability

Absolute summability of trigonometric series

1981 ◽  
Vol 30 (6) ◽  
pp. 912-919
Author(s):  
I. Szalay
Keyword(s):  
Trigonometric Series ◽  
Absolute Summability

scholarly journals On Absolute Summability for any Positive Order

1933 ◽  
Vol 3 (3) ◽  
pp. 173-178 ◽  
Author(s):  
C. E. Winn
Keyword(s):  
Absolute Summability ◽  
Positive Order ◽  
Partial Sum ◽  
Image Position

Absolute summability according to Cesàro's method has been defined by Fekete for positive integral orders, as follows:—Denoting the rth partial sum of a series Σun by and its rth mean, namely2, by we can regard as the sum of the series.

scholarly journals Characterization on some absolute summability factors of infinite series

1999 ◽  
Vol 22 (4) ◽  
pp. 817-822
Author(s):  
W. T. Sulaiman
Keyword(s):  
Infinite Series ◽  
General Theorem ◽  
Absolute Summability ◽  
Summability Factors ◽  
Absolute Summability Factors

A general theorem concerning some absolute summability factors of infinite series is proved. This theorem characterizes as well as generalizes our previous result [4]. Other results are also deduced.

scholarly journals Absolute summability of power $p$ of series, associated with conjugate Fourier series, by triangular matrix methods

2021 ◽  
pp. 54
Author(s):  
N.I. Volkova ◽  
N.S. Novikova
Keyword(s):  
Fourier Series ◽  
Triangular Matrix ◽  
Absolute Summability ◽  
Matrix Methods ◽  
Conjugate Fourier Series

We establish conditions of absolute summability of powers of series that are associated with conjugate Fourier series, by triangular matrix methods, and provide the application of the theorems proved to Voronoi-Nerlund method.

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