A matrix application of power increasing sequences to infinite series and Fourier series

  • Şebnem Yıldız Department of Mathematics, Ahi Evran University, Kırşehir, Turkey


UDC 517.54

The aim of the paper is a generalization, under weaker conditions, of the main theorem on quasi-$\sigma$-power increasing sequences applied to $|A,\theta_{n}|_{k}$ summability factors of infinite series and Fourier series. We obtain some new and known results related to basic summability methods.


Bari, N. K.; Stečkin, S. B. Best approximations and differential properties of two conjugate functions. (Russian) Trudy Moskov. Mat. Obšč. 5 (1956), 483–522.

Bor, Hüseyin. On two summability methods. Math. Proc. Cambridge Philos. Soc. 97 (1985), no. 1, 147–149. https://doi.org/10.1017/s030500410006268x

Bor, Hüseyin. On the relative strength of two absolute summability methods. Proc. Amer. Math. Soc. 113 (1991), no. 4, 1009–1012. https://doi.org/10.1090/s0002-9939-1991-1068115-x

Bor, Hüseyin. A study on weighted mean summability. Rend. Circ. Mat. Palermo (2) 56 (2007), no. 2, 198–206. https://doi.org/10.1007/bf03031439

Bor, Hüseyin. On absolute weighted mean summability of infinite series and Fourier series. Filomat 30 (2016), no. 10, 2803–2807. https://doi.org/10.2298/fil1610803b

Bor, Hüseyin. Some new results on absolute Riesz summability of infinite series and Fourier series. Positivity 20 (2016), no. 3, 599–605. https://doi.org/10.1007/s11117-015-0374-0

Bor, Hüseyin. An application of power increasing sequences to infinite series and Fourier series. Filomat 31 (2017), no. 6, 1543–1547. https://doi.org/10.2298/fil1706543b

Cesàro, E. Sur la multiplication des séries, Bull. Sci. Math., 14 (1890), 114–120.

Chen, Kien-Kwong. Functions of bounded variation and the Cesaro means of a Fourier series. Acad. Sinica Science Record 1, (1945). 283–289.

Flett, T. M. On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. London Math. Soc. (3) 7 (1957), 113–141. https://doi.org/10.1112/plms/s3-7.1.113

Hardy, G. H. Divergent Series. Oxford, at the Clarendon Press, 1949. xvi+396 pp.

Kogbetliantz, E. Sur lès series absolument sommables par la methode des moyennes arithmetiques, Bull. Sci. Math., 49 (1925), 234–256.

Leindler, L. A new application of quasi power increasing sequences. Publ. Math. Debrecen 58 (2001), no. 4, 791–796. https://hungary.pure.elsevier.com/en/publications/a-new-application-of-quasi-power-increasing-sequences

Özarslan, H. S.; Kandefer, T. On the relative strength of two absolute summability methods. J. Comput. Anal. Appl. 11 (2009), no. 3, 576–583.

Sarıgöl, Mehmet Ali. On the local properties of factored Fourier series. Appl. Math. Comput. 216 (2010), no. 11, 3386–3390. https://doi.org/10.1016/j.amc.2010.04.070

Sulaiman, W. T. Inclusion theorems for absolute matrix summability methods of an infinite series. IV. Indian J. Pure Appl. Math. 34 (2003), no. 11, 1547–1557. https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/2000c4ed_1547.pdf

Sulaiman, W. T. Some new factor theorem for absolute summability. Demonstratio Math. 46 (2013), no. 1, 149–156. https://doi.org/10.1515/dema-2013-0429

Tanović-Miller, N. On strong summability. Glasnik Mat. Ser. III 14(34) (1979), no. 1, 87–97. https://books.google.hr/books?id=0d3gcacGQRYC&pg=PA87#v=onepage&q&f=false

Yildiz, Şebnem. A new theorem on absolute matrix summability of Fourier series. Publ. Inst. Math. (Beograd) (N.S.) 102(116) (2017), 107–113. https://doi.org/10.2298/pim1716107y

Yıldız, Ş. On absolute matrix summability factors of infinite series and Fourier series, GU J. Sci., 30 (2017), no. 1, 363–370. https://www.researchgate.net/deref/http%3A%2F%2Fdx.doi.org%2F10.1134%2FS0001434618010303

Yıldız, Ş. On the absolute matrix summability factors of Fourier series. Math. Notes 103 (2018), no. 1-2, 297–303. https://doi.org/10.1134/s0001434618010303

How to Cite
Yıldız Şebnem. “A Matrix Application of Power Increasing Sequences to Infinite Series and Fourier Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 5, Apr. 2020, pp. 635–643, doi:10.37863/umzh.v72i5.6016.
Research articles