Tauberian theorems for generalized Abelian summability methods

1999 ◽  
pp. 13-26 ◽  
Author(s):  
Časlav V. Stanojević ◽  
I. Canak ◽  
V. B. Stanojević
Keyword(s):  
Tauberian Theorems ◽  
Summability Methods

scholarly journals Some Tauberian theorems for Euler and Borel summability

1980 ◽  
Vol 3 (4) ◽  
pp. 731-738 ◽  
Author(s):  
J. A. Fridy ◽  
K. L. Roberts
Keyword(s):  
Matrix Method ◽  
Tauberian Theorems ◽  
Borel Summability ◽  
Summability Methods

The well-known summability methods of Euler and Borel are studied as mappings fromℓ1intoℓ1. In thisℓ−ℓsetting, the following Tauberian results are proved: ifxis a sequence that is mapped intoℓ1by the Euler-Knopp methodErwithr>0(or the Borel matrix method) andxsatisfies∑n=0∞|xn−xn+1|n<∞, thenxitself is inℓ1.

scholarly journals Tauberian Theorems for the Product of Weighted and Cesàro Summability Methods for Double Sequences

2019 ◽  
Vol 38 (7) ◽  
pp. 9-19
Author(s):  
Gökşen Fındık ◽  
İbrahim Çanak
Keyword(s):  
Double Sequence ◽  
Sufficient Conditions ◽  
Complex Numbers ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Tauberian Conditions ◽  
Summability Methods ◽  
Cesaro Summability ◽  
Necessary And Sufficient

In this paper, we obtain necessary and sufficient conditions, under which convergence of a double sequence in Pringsheim's sense follows from its weighted-Cesaro summability. These Tauberian conditions are one-sided or two-sided if it is a sequence of real or complex numbers, respectively.

Tauberian theorems invariant for a product of two summability methods

1960 ◽  
Vol 73 (3) ◽  
pp. 256-267
Author(s):  
M. R. Parameswaran ◽  
C. T. Rajagopal
Keyword(s):  
Tauberian Theorems ◽  
Summability Methods
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