Factors for \(|\overline N,p_ n;\delta|_ k\) summability of Fourier series
type: Item
instance of: scholarly article
title: Factors for \(|\overline N,p_ n;\delta|_ k\) summability of Fourier series
zbMATH Open document ID: 0780.42010
DOI: 10.1007/BF02837179
author: Hüseyin Bor
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1993-01-16T00:00:00Z
review text: The author first establishes a theorem on summability factors of a series \(\sum a_ n\) for \(| \overline N,p_ n;\delta |_ k\) summability. He then uses it to obtain a result for Fourier series of \(f(x)\) under the condition ``\(\varphi_ 1(t) \in BV(0,\pi)\)'', where \(\varphi_ 1(t)={1 \over 2t} \int^ t_ 0\{f(x+u)+f(x-u)\}du\). These results extend his previous results [Bull. Inst. Math., Acad. Sin. 17, No. 3, 285-290 (1985; Zbl 0696.42007)] on summability \(| \overline N,p_ n |_ k\), \(k \geq 1\).
Mathematics Subject Classification ID: 42A20
Mathematics Subject Classification ID: 40D15
zbMATH DE Number: 92805
zbMATH Keywords: absolute summability factors
zbMATH Keywords: factors
zbMATH Keywords: Fourier series
reviewed by: S. M. Mazhar
MaRDI profile type: Publication
cites work: A Note on Two Summability Methods
cites work: Q3480641
cites work: Absolute summability factors for infinite series
cites work: Q3472624
cites work: The summability factors of a Fourier series
full work available at URL: https://doi.org/10.1007/bf02837179
OpenAlex ID: W2352871171
description: scientific article; zbMATH DE number 92805