An absolute matrix summability of infinite series and Fourier series
Resumo
The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power sequences.
Downloads
Referências
Bari, N. K., Steckin, S.B, Best approximation and differential properties of two conjugate functions. Trudy. Moskov. Mat. Obsc. (in Russian) 5, 483-522 (1956)
Bor, H., On two summability methods. Math. Proc. Cambridge Philos Soc. 97, 147-149 (1985)
https://doi.org/10.1017/S030500410006268X
Bor, H., Quasi-monotone and almost increasing sequences and their new applications. Abstr. Appl. Anal. Art. ID 793548, 6 PP.(2012)
Bor, H., On absolute weighted mean summability of infinite series and Fourier series. Filomat 30, 2803-2807 (2016)
https://doi.org/10.2298/FIL1610803B
Bor, H., Some new results on absolute Riesz summablity of infinite series and Fourier series. Positivity 20, 3 599-605 (2016)
https://doi.org/10.1007/s11117-015-0374-0
Bor, H., An Application of power increasing sequences to infinite series and Fourier series. Filomat 31, 1543-1547 (2017)
https://doi.org/10.2298/FIL1706543B
Bor, H., Absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series. Filomat 31, 15 4963-4968 (2017)
https://doi.org/10.2298/FIL1715963B
Cesaro, E., Sur la multiplication des series. Bull. Sci. Math. 14, 114-120 (1890)
Chen, K. K., Functions of bounded variation and the cesaro means of Fourier series. Acad. Sin. Sci. Record 1 283-289 (1945)
Flett, T. M., On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. Lond. Math. Soc. 7, 113-141 (1957)
https://doi.org/10.1112/plms/s3-7.1.113
Hardy, G. H., Divergent Series. Clarendon Press, Oxford (1949)
Kogbetliantz, E., Sur les series absolument sommables par la methode des moyennes arithmetiques. Bull. Sci. Math. 49, 234-256 (1925)
Leindler, L., A new application of quasi power increasing sequences. Publ. Math. Debrecen 58, 791-796 (2001)
Mazhar, S. M., Absolute summability factors of infinite series. Kyungpook Math. J. 39, 67-73 (1999)
Ozarslan, H. S., Yıldız, S¸., A new study on the absolute summability factors of Fourier series. J. Math. Anal. 7 31-36 (2016)
https://doi.org/10.2298/FIL1715897O
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)
Sulaiman, W. T., Extension on absolute summability factors of infinite series. J. Math. Anal. Appl. 322, 1224-1230 (2006)
https://doi.org/10.1016/j.jmaa.2005.09.019
Tanovic-Miller, N., On strong summability. Glas. Mat. Ser III 14 , (34) 87-97 (1979)
Yildiz, S., New variations of power increasing sequences, arXiv:1711.04470v1 [math.FA], 13 Nov (2017)
Yildiz, S., A New Note on General Matrix Application of Quasi-monotone Sequences, Filomat, vol 32: no 10: 3709-3715 (2018)
https://doi.org/10.2298/FIL1810709Y
Yildiz, S., On the Absolute Matrix Summability Factors of Fourier Series, Mathematical Notes, 103 (1-2):297-303 (2018)
https://doi.org/10.1134/S0001434618010303
Yıldız, S., On application of matrix summability to Fourier series, Mathematical Methods in the Applied Sciences, 41 (2) 664-670 (2018)
Yildiz, S., Absolute matrix summability factors of Fourier series with quasi-f-power increasing sequences, Electronic Notes in Discrete Math., 67 37-41, (2018)
https://doi.org/10.1016/j.endm.2018.05.007
Yildiz, S. A matrix application on absolute weighted arithmetic mean summability factors of infinite series, Tibilisi Math.J., (11) 2 59-65 (2018)
https://doi.org/10.32513/tbilisi/1529460022
Yildiz, S. A new result on weighted arithmetic mean summability of almost increasing sequences, 2nd International Conference of Mathematical Sciences (ICMS 2018), Maltepe University, 31 July 2018-6 August 2018.
Yildiz, S., A Matrix Application of Power Increasing Sequences to Infinite Series and Fourier Series, Ukranian Mathematical Journal,(in press)
Yildiz, S., A New Note on General Matrix Application of Quasi-monotone Sequences, Filomat, 32, 3709-3715 (2019)
Copyright (c) 2019 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).