general summability
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Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3093-3096
Author(s):  
Hüseyin Bor

Quite recently, in [10], we have proved a theorem dealing with the generalized absolute Ces?ro summability factors of infinite series by using quasi monotone sequences and quasi power increasing sequences. In this paper, we generalize this theorem for the more general summability method. This new theorem also includes some new and known results.


2016 ◽  
Vol 15 (01) ◽  
pp. 107-121 ◽  
Author(s):  
Ferenc Weisz

In this paper, a general summability method of multi-dimensional Fourier transforms, the so-called [Formula: see text]-summability, is investigated. It is shown that if [Formula: see text] is in a Herz space, then the summability means [Formula: see text] of a function [Formula: see text] converge to [Formula: see text] at each modified Lebesgue point, whenever [Formula: see text] and [Formula: see text] is in a cone. The same holds for Fourier series. Some special cases of the [Formula: see text]-summation are considered, such as the Weierstrass, Abel, Picard, Bessel, Fejér, Cesàro, de la Vallée-Poussin, Rogosinski and Riesz summations.


2015 ◽  
Vol 61 (1) ◽  
pp. 123-128
Author(s):  
Ibrahim Çanak

Abstract We investigate conditions under which Mϕ summability implies Abel summability and give the generalized Littlewood Tauberian theorem for Mϕ summability method.


2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Uaday Singh ◽  
M. L. Mittal ◽  
Smita Sonker

Various investigators such as Khan (1974), Chandra (2002), and Liendler (2005) have determined the degree of approximation of 2π-periodic signals (functions) belonging to Lip(α,r)class of functions through trigonometric Fourier approximation using different summability matrices with monotone rows. Recently, Mittal et al. (2007 and 2011) have obtained the degree of approximation of signals belonging to Lip(α,r)- class by general summability matrix, which generalize some of the results of Chandra (2002) and results of Leindler (2005), respectively. In this paper, we determine the degree of approximation of functions belonging to Lip αandW(Lr,ξ(t)) classes by using Cesáro-Nörlund(C1·Np)summability without monotonicity condition on{pn}, which in turn generalizes the results of Lal (2009). We also note some errors appearing in the paper of Lal (2009) and rectify them in the light of observations of Rhoades et al. (2011).


2011 ◽  
Vol 218 (3) ◽  
pp. 1046-1051
Author(s):  
Hamdullah Şevli˙ ◽  
Ekrem Savaş

2008 ◽  
Vol 145 (2) ◽  
pp. 419-442 ◽  
Author(s):  
FERENC WEISZ

AbstractA general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebraW(C,ℓ1)($\mathbb{R}$d). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from theHpHardy space toLp(orHp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.


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