Abstract
In this paper, a known theorem on $\left|\bar{N},p_{n}\right|_{k}$ summability factors of infinite series have been generalized for $\varphi-\left|A,p_{n}\right|_{k}$ summability factors. Using this theorem, some new results dealing with Fourier series have been obtained.
Keywords
Summability factors absolute matrix summability Fourier series infinite series H\"{o}lder inequality.
References
- bibitem{Hb}Bor, H., ''On two summability methods'', Math. Proc. Cambridge Philos. Soc., 97:147-149, (1985).
- bibitem{HB} Bor, H., ''Multipliers for $|bar{N},p_{n}|_{k}$ summability of Fourier series'', Bull. Inst. Math. Acad.
- Sinica, 17:285-290, (1989).
- bibitem{bor1991b} Bor, H., ''On the relative strength of two absolute summability methods'', Proc. Amer.
- Math. Soc., 113:1009-1012, (1991).
- bibitem{Boo} Bor, H., ''Some new results on infinite series and Fourier series'', Positivity, 19:467-473, (2015).
- bibitem{HBr2} Bor, H., ''Some new results on absolute Riesz summability of infinite series and Fourier series'', Positivity, 20:599-605, (2016).
- bibitem{Fl} Flett, T. M., ''On an extension of absolute summability and some theorems of Littlewood and Paley'', Proc. Lond. Math. Soc., 7:113-141, (1957).
- bibitem{Ha} Hardy, G. H., Divergent Series, Oxford University Press, Oxford (1949).
- bibitem{Mi} Mishra, K. N., ''Multipliers for $|bar{N},p_{n}|$ summability of Fourier series'', Bull. Inst. Math. Acad. Sinica, 14:431-438, (1986).
- bibitem{HK} "{O}zarslan, H. S. and "{O}u{g}d"{u}k, H. N., ''Generalizations of two theorems on absolute summability methods'', Aust. J. Math. Anal. Appl., 13:7pp., (2004).
- bibitem{ozarslanyildiz1} "{O}zarslan, H. S. and Y{i}ld{i}z, c{S}., ''Local properties of absolute matrix summability of factored Fourier series'', Filomat, (2016) (in press).
- bibitem{ozarslanyildiz} "{O}zarslan, H. S. and Y{i}ld{i}z, c{S}., ''A new study on the absolute summability factors of Fourier series'', J. Math. Anal., 7:31-36, (2016).
- bibitem{yildiz2} Y{i}ld{i}z, c{S}., ''A new theorem on absolute matrix summability of Fourier series'', Pub. De Inst. Math., (2016) (in press).
- bibitem{Su} Sulaiman, W. T., ''Inclusion theorems for absolute matrix summability methods of an infinite series'', IV, Indian J. Pure Appl. Math., 34 (11):1547-1557, (2003).
Abstract
References
- bibitem{Hb}Bor, H., ''On two summability methods'', Math. Proc. Cambridge Philos. Soc., 97:147-149, (1985).
- bibitem{HB} Bor, H., ''Multipliers for $|bar{N},p_{n}|_{k}$ summability of Fourier series'', Bull. Inst. Math. Acad.
- Sinica, 17:285-290, (1989).
- bibitem{bor1991b} Bor, H., ''On the relative strength of two absolute summability methods'', Proc. Amer.
- Math. Soc., 113:1009-1012, (1991).
- bibitem{Boo} Bor, H., ''Some new results on infinite series and Fourier series'', Positivity, 19:467-473, (2015).
- bibitem{HBr2} Bor, H., ''Some new results on absolute Riesz summability of infinite series and Fourier series'', Positivity, 20:599-605, (2016).
- bibitem{Fl} Flett, T. M., ''On an extension of absolute summability and some theorems of Littlewood and Paley'', Proc. Lond. Math. Soc., 7:113-141, (1957).
- bibitem{Ha} Hardy, G. H., Divergent Series, Oxford University Press, Oxford (1949).
- bibitem{Mi} Mishra, K. N., ''Multipliers for $|bar{N},p_{n}|$ summability of Fourier series'', Bull. Inst. Math. Acad. Sinica, 14:431-438, (1986).
- bibitem{HK} "{O}zarslan, H. S. and "{O}u{g}d"{u}k, H. N., ''Generalizations of two theorems on absolute summability methods'', Aust. J. Math. Anal. Appl., 13:7pp., (2004).
- bibitem{ozarslanyildiz1} "{O}zarslan, H. S. and Y{i}ld{i}z, c{S}., ''Local properties of absolute matrix summability of factored Fourier series'', Filomat, (2016) (in press).
- bibitem{ozarslanyildiz} "{O}zarslan, H. S. and Y{i}ld{i}z, c{S}., ''A new study on the absolute summability factors of Fourier series'', J. Math. Anal., 7:31-36, (2016).
- bibitem{yildiz2} Y{i}ld{i}z, c{S}., ''A new theorem on absolute matrix summability of Fourier series'', Pub. De Inst. Math., (2016) (in press).
- bibitem{Su} Sulaiman, W. T., ''Inclusion theorems for absolute matrix summability methods of an infinite series'', IV, Indian J. Pure Appl. Math., 34 (11):1547-1557, (2003).
Details
| Journal Section | Mathematics |
|---|---|
| Authors | |
| Publication Date | March 14, 2017 |
| Published in Issue | Year 2017 Volume: 30 Issue: 1 |