Results 1 to 10 of about 406 (262)

Orlicz–Pettis Theorem through Summability Methods

Mathematics, 2019
This paper unifies several versions of the Orlicz−Pettis theorem that incorporate summability methods. We show that a series is unconditionally convergent if and only if the series is weakly subseries convergent with respect to a regular linear ...
Fernando León-Saavedra, Maria Del Pilar Romero De La Rosa, Antonio Sala   +2 more
exaly   +3 more sources

Absolute φ − | C , α , β ; δ | k $\varphi- \vert C, \alpha, \beta; \delta\vert _{k}$ summability of infinite series [PDF]

Journal of Inequalities and Applications, 2017
In this paper, we established a generalized theorem on a minimal set of sufficient conditions for absolute summability factors by applying a sequence of a wider class (quasi-power increasing sequence) and the absolute Cesàro φ − | C , α , β ; δ | k ...
Smita Sonker, Alka Munjal
doaj   +2 more sources

Partial best approximations and the absolute Cesaro summability of multiple Fourier series [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2021
The article is devoted to the problem of absolute Cesaro summability of multiple trigonometric Fourier series. Taking a central place in the theory of Fourier series this problem was developed quite widely in the one-dimensional case and the ...
S. Bitimkhan, D.T. Alibieva
doaj   +3 more sources

A new extension on the theorem of Bor

Comptes Rendus. Mathématique, 2021
In [8], Bor has obtained a main theorem dealing with Riesz summability factors of infinite series and Fourier series. In this paper, we generalized that theorem to $|A,\theta _{n}|_{k}$ summability method for taking power increasing sequence.
Yıldız, Şebnem
doaj   +1 more source

A Study on Generalized Absolute Matrix Summability

Cumhuriyet Science Journal, 2022
In the present paper, generalized absolute matrix summability method of infinite series has been studied. A known theorem on IMI ,summability method has been generalized using the summability method of infinite series.
Ahmet Karakaş
doaj   +1 more source

A new note on factored infinite series and trigonometric Fourier series

Comptes Rendus. Mathématique, 2021
In this paper, we have proved two main theorems under more weaker conditions dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series.
Bor, Hüseyin
doaj   +1 more source

Pythagorean harmonic summability of Fourier series

Demonstratio Mathematica, 2021
This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with the introduction of new concepts like the smoothing operator and semi-harmonic summation ...
Haidar Nassar H. S.
doaj   +1 more source

On |A|k summability factors of infinite series; pp. 201–206 [PDF]

Proceedings of the Estonian Academy of Sciences, 2010
In an earlier paper (Rhoades, B. E. and Savaş, E. Some necessary conditions for absolute matrix summability factors. Indian J. Pure Appl. Math., 2002, 33(7), 1003–1009) the authors obtained necessary conditions for the series ∑ an to be absolutely ...
B. E. Rhoades, Ekrem Savaş
doaj   +1 more source

On the Cesáro Summability of Double Series [PDF]

Journal of Inequalities and Applications, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Savaş, Ekrem, Şevli, Hamdullah, Rhoades, B. E.   +2 more
openaire   +4 more sources

On the degree of approximation of Fourier series based on a certain class of product deferred summability means

Journal of Inequalities and Applications, 2023
In this article, we first introduce and study the basic concepts of deferred Euler and deferred Nörlund product summability means of Fourier series of arbitrary periodic functions.
Bidu Bhusan Jena, Susanta Kumar Paikray, M. Mursaleen   +2 more
doaj   +1 more source