On absolute weighted arithmetic mean summability of infinite series and Fourier series
- 24 March 2022
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 150 (8), 3517-3523
- https://doi.org/10.1090/proc/15927
Abstract
Quite recently, we have obtained two main theorems dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series [C. R. Math. Acad. Sci. Paris 359 (2021), pp. 323-328]. In this paper, we have generalized these theorems for a general summability method. We have also obtained some new and known results for certain absolute summability methods.Keywords
This publication has 20 references indexed in Scilit:
- On the Absolute Matrix Summability Factors of Fourier SeriesMathematical Notes, 2018
- On absolute Riesz summability factors of infinite series and their application to Fourier seriesGeorgian Mathematical Journal, 2017
- An application of quasi-monotone sequences to infinite series and Fourier seriesAnalysis and Mathematical Physics, 2017
- On the Absolute Riesz Summability FactorsRocky Mountain Journal of Mathematics, 1994
- On Some Summability Factors of Infinite SeriesProceedings of the American Mathematical Society, 1992
- On the Relative Strength of Two Absolute Summability MethodsProceedings of the American Mathematical Society, 1991
- On two summability methodsMathematical Proceedings of the Cambridge Philosophical Society, 1985
- An aspect of local property of $\vert R,\,{\rm log}\,n,\,1\vert $ summability of Fourier seriesTohoku Mathematical Journal, 1959
- On an Extension of Absolute Summability and Some Theorems of Littlewood and PaleyProceedings of the London Mathematical Society, 1957
- Notes on Fourier analysis (XVIII): Absolute summability of series with constant termsTohoku Mathematical Journal, 1949