A NEW STUDY ON THE ABSOLUTE SUMMABILITY FACTORS OF FOURIER SERIES
DOI:
https://doi.org/10.5281/dp8z8e06Abstract
In this paper, we establish a new theorem on | A, pn |k summability factors of Fourier series using matrix transformation, which generalizes a main theorem of Bor [6] on N, p ¯ n k summability factors of Fourier series. Also some new results have been obtained
References
[1] H. Bor, On two summability methods, Math. Proc. Cambridge Philos Soc. 97 (1985), 147-149.
[2] H. Bor, Multipliers for N, p ¯ n k summability of Fourier series, Bull. Inst. Math. Acad. Sinica 17 (1989), 285-290.
[3] H. Bor, On the relative strength of two absolute summability methods, Proc. Amer. Math.
Soc. 113 (1991), 1009-1012. A NEW STUDY ON THE ABSOLUTE SUMMABILITY FACTORS OF FOURIER SERIES by virtue of the hypotheses of Theorem 3.1 and Lemma 3.2. Now, using H¨older’s inequality, we have that 35
[4] H. Bor, On the local property of N, p ¯ n k summability of factored Fourier series, J. Math. Anal. Appl. 163 (1992), 220-226.
[5] H. Bor, Local properties of Fourier series, Int. J. Math. Math. Sci. 23 (2000), 703-709.
[6] H. Bor, On the absolute summability factors of Fourier series, J. Comp. Anal. Appl. 8 (2006),
223-227.
[7] H. Bor, Some new results on infinite series and Fourier series, Positivity 19 (2015), 467-473.
[8] H. Bor, Some new results on absolute Riesz summability of infinite series and Fourier series,
Positivity 20, (2016), (in press).
[9] D. Borwein, The nonlocal nature of the summability of Fourier series by certain absolute
Riesz methods, Proc. Amer. Math. Soc. 114 (1992), 89-94 .
[10] G. H. Hardy, Divergent Series, Oxford Univ. Press, Oxford, (1949).
[11] K. N. Mishra, Multipliers for N, p ¯ n k summability of Fourier series, Bull. Inst. Math. Acad. Sinica 14 (1986), 431-438.
[12] H. S. Ozarslan, ¨ A note on | N, p ¯ n |k summability factors, Int. J. Pure Appl. Math. 13 (2004), 485–490.
[13] W. T. Sulaiman, Inclusion theorems for absolute matrix summability methods of an infinite series. IV, Indian J. Pure Appl. Math. 34 (11) (2003), 1547-1557.
[14] N. Tanovi˘c-Miller, On strong summability, Glas. Mat. Ser. III 14 (34) (1979), 87-97.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Journal of Mathematical Analysis
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Author(s) and co-author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties and that the Article has not been published elsewhere. Author(s) agree to the terms that the JMA Journal will have the full right to remove the published article on any misconduct found in the published article.
