An absolute matrix summability of infinite series and Fourier series

Resumen

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.

Descargas

La descarga de datos todavía no está disponible.

Biografía del autor/a

Sebnem Yildiz, Ahi Evran University

Mathematics

 

Citas

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)

https://doi.org/10.2298/FIL1810709Y

Publicado
2019-10-14