A study on absolute summability factors

Year 2020, , 220 - 223, 01.02.2020

G. Canan Hazar Güleç

https://doi.org/10.16984/saufenbilder.642406

Abstract

In this study we proved theorems dealing with
summability factors giving relations between absolute Cesàro and absolute weighted
summability methods. So we deduced some results in the special cases.

Keywords

Summability factors, Absolute Cesàro summability, Absolute weighted summability

References

• [1] H. Bor, “Some equivalence theorems on absolute summability methods,” Acta Math. Hung., vol. 149, pp.208-214, 2016.[2] H. Bor, “On two summability methods,” Math. Proc. Cambridge Philos Soc., vol. 98, 147-149, 1985. [3] T.M. Flett, “On an extension of absolute summability and some theorems of Littlewood and Paley,” Proc. London Math. Soc., vol. 7, pp. 113-141, 1957.[4] Hazar Güleç, G.C. (in press).Summability factor relations between absolute weighted and Cesàro means, Mathematical Methods in the Applied Sciences. (DOI: 10.1002/mma.5399).[5] G.C. Hazar and M.A. Sarıgöl, “Compact and Matrix Operators on the Space |C,-1|_k,” J. Comput. Anal. Appl., vol.25, no.6, pp. 1014-1024, 2018.[6] G.C. Hazar, and M.A. Sarıgöl, “On factor relations between weighted and Nörlund means,” Tamkang J. Math. (in press).[7] I.J. Maddox, “Elements of functinal analysis, Cambridge University Press,” London, New York, 1970.[8] S.M. Mazhar, “On the absolute summability factors of infinite series,” Tohoku Math. J., vol.23, pp.433-451, 1971.[9] M.R. Mehdi, “Summability factors for generalized absolute summability I,” Proc. London Math. Soc., vol.3., no.10, pp.180-199, 1960.[10] R.N. Mohapatra, “On absolute Riesz summability factors,” J. Indian Math. Soc., vol.32, pp.113-129, 1968.[11] M. A. Sarıgöl, “Spaces of series Summable by absolute Cesàro and Matrix Operators ,” Comm. Math. Appl. , vol.7, no.1, pp.11-22, 2016.[12] M.A. Sarıgöl, “Extension of Mazhar's theorem on summability factors,” Kuwait J. Sci., vol.42, no.3, pp.28-35, 2015.[13] M.A. Sarıgöl, “On the local properties of factored Fourier series,” Appl. Math. Comp., vol.216, pp.3386-3390, 2010. [14] W.T. Sulaiman, “On summability factors of infinite series,” Proc. Amer. Math. Soc., vol.115, pp.313-317, 1992.[15] W.T. Sulaiman, “On some absolute summability factors of Infinite Series,” Gen. Math. Notes, vol.2, no.2, pp.7-13, 2011.[16] B. Thorpe, “Matrix transformations of Cesàro summable Series,” Acta Math. Hung., vol. 48(3-4), pp.255-265, 1986.