A Tauberian Theorem for the Power-Series Summability Method

2018 ◽  
Vol 69 (12) ◽  
pp. 1981-1996
Author(s):  
Ü. Totur ◽  
İ. Çanak
Keyword(s):  
Power Series ◽  
Tauberian Theorem ◽  
Summability Method

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

A Tauberian theorem for power series

2001 ◽  
Vol 77 (4) ◽  
pp. 354-359 ◽  
Author(s):  
T. Hilberdink
Keyword(s):  
Power Series ◽  
Tauberian Theorem

A Tauberian Theorem for Borel-Type Methods of Summability

1969 ◽  
Vol 21 ◽  
pp. 740-747 ◽  
Author(s):  
D. Borwein
Keyword(s):  
Tauberian Theorem ◽  
Convergent Series ◽  
Summability Method ◽  
Negative Integer ◽  
Exponential Method ◽  
Image Position ◽  
Borel Type ◽  
Cesàro Method

Suppose throughout that α >0, β is real, and Nis a non-negative integer such that αN+ β> 0. A series of complex terms is said to be summable (B, α,β) to l if, as x→ ∞,where sn= a0 + a1 + … + an.The Borel-type summability method (B, α, β) is regular, i.e., all convergent series are summable (B, α,β) to their natural sums; and (B,1, 1) is the standard Borel exponential method B.Our aim in this paper is to prove the following Tauberian theorem.THEOREM. Iƒ(i) p ≧ – ½, an = o(np), and(ii) is summable (B, α,β) to l, then the series is summable by the Cesaro method(C, 2p + 1) to l.

A Multiplicative Analogue of Schur's Tauberian Theorem

2003 ◽  
Vol 46 (3) ◽  
pp. 473-480 ◽  
Author(s):  
Karen Yeats
Keyword(s):  
Power Series ◽  
Asymptotic Behaviour ◽  
Dirichlet Series ◽  
Tauberian Theorem ◽  
Partial Sums ◽  
Regularly Varying Functions ◽  
Regularly Varying

AbstractA theorem concerning the asymptotic behaviour of partial sums of the coefficients of products of Dirichlet series is proved using properties of regularly varying functions. This theorem is a multiplicative analogue of Schur's Tauberian theorem for power series.

XXII.—On Methods of Summability Based on Power Series

1957 ◽  
Vol 64 (4) ◽  
pp. 342-349
Author(s):  
D. Borwein
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Radius Of Convergence ◽  
Main Concern ◽  
Image Position

SynopsisGiven a power series with real non-negative coefficients and having radius of convergence p, a summability method P is defined as follows:The main concern of this note is to establish conditions sufficient for one such method to include another.

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