scholarly journals APPLICATIONS OF MATRIX TRANSFORMATIONS TO ABSOLUTE SUMMABILITY

2021 ◽  
pp. 1381
Author(s):  
Mehmet Ali Sarigol
Keyword(s):  
Absolute Summability ◽  
Matrix Transformations ◽  
The Absolute

Rhoades and Sava¸s [6],[11] established necessary for inclusions of the absolute matrix summabilities under additional conditions. In this paper we determine necessary or su¢ cient conditions for some classes of in…nite matrices, and using this get necessary or su¢ cient conditions for more general absolute summabilities applied to all matrices.

On the absolute summability of Fourier multiple series

1972 ◽  
Vol 23 (3) ◽  
pp. 291-304
Author(s):  
Yu. A. Ponomarenko ◽  
M. F. Timan
Keyword(s):  
Absolute Summability ◽  
Multiple Series ◽  
The Absolute

Extension of Maddox’s space l(μ) with Nörlund means

2019 ◽  
Vol 12 (06) ◽  
pp. 2040005
Author(s):  
Fadime Gökçe ◽  
Mehmet Ali Sarigöl
Keyword(s):  
Acta Math ◽  
Summability Method ◽  
Schauder Basis ◽  
Matrix Transformations ◽  
Topological Structures ◽  
Nörlund Means ◽  
Series Space ◽  
The Absolute ◽  
Matrix Operators ◽  
Absolute Nörlund Summability

In this paper, we introduce a new series space [Formula: see text] as the set of all series summable by the absolute Nörlund summability method, which includes the spaces [Formula: see text] and [Formula: see text] of Maddox [Spaces of strongly summable sequences, Quart. J. Math. 18(1) (1967) 345–355], Sarıgöl [Spaces of series summable by absolute Cesàro and matrix operators, Comm. Math Appl. 7(1) (2016) 11–22], Hazar and Sarıgöl [On absolute Nörlund spaces and matrix operators, Acta Math. Sinica, (English Ser.) 34(5) (2018) 812–826], respectively. Also, we study its some algebraic and topological structures such as isomorphism, the [Formula: see text], [Formula: see text], [Formula: see text] duals, Schauder basis, and characterize certain matrix transformations on that space.

On the absolute summability of some series related to a Fourier series

1970 ◽  
Vol 67 (1) ◽  
pp. 29-45 ◽  
Author(s):  
B. K. Ray
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Absolute Summability ◽  
The Absolute ◽  
Image Position

1.Introduction. 1.1. Let f(t) be a periodic function with period 2π and integrable in the Lebesgue sense over ( -π,π). We assume as we may without loss of generality, that the Fourier series of f(t) is .

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