Some New Results on Absolute Summability Factors

Abstract

In this paper, we establish the general summability factors theorems related to generalized absolute Cesàro  and  factorable matrix summability methods for . Also some new results for absolute Cesàro  and weighted means are obtained as corollaries

Keywords

• Absolute Cesàro summability,Factorable matrix,Matrix methods,Sequence spaces

References

1. 1. Sulaiman, W.T., “On some summability factors of infinite series”, Proc. Amer. Math. Soc., 115: 313-317, (1992).
2. 2. Bor, H., “On two summability methods”, Math. Proc. Cambridge Philos Soc., 97: 147-149, (1985).
3. 3. Sarıgöl, M.A., “On two absolute Riesz summability factors of infinite series” Proc. Amer. Math. Soc.,118: 485-488, (1993).
4. 4. Sarıgöl, M. A., “ On absolute factorable matrix summability methods” , Bull. Math. Anal. Appl., 8: 1-5, (2016).
5. 5. Borwein, D., “Theorems on some methods of summability”, Quart. J. Math. Oxford Ser. (2), 9: 310-314, (1958).
6. 6. Das, G., “A Tauberian theorem for absolute summability”, Proc. Camb. Phil. Soc., 67: 321-326, (1970).
7. 7. Flett, T.M., “On an extension of absolute summability and some theorems of Littlewood and Paley”, Proc. London Math. Soc., 7:113-141, (1957).
8. 8. Mazhar, S.M. “On the absolute summability factors of infinite series”, Tohoku Math. J., 23: 433-451, (1971).

9. 9. Mehdi, M.R., “Summability factors for generalized absolute summability I”, Proc. London Math. Soc., 10(3): 180-199, (1960).
10. 10. Mohapatra, R.N., “On absolute Riesz summability factors”, J. Indian Math. Soc., 32: 113-129, (1968).
11. 11. Bor, H., “Some equivalence theorems on absolute summability methods”, Acta Math. Hung., 149: 208-214, (2016).
12. 12. Hazar Güleç, G.C., Sarıgöl, M.A., “On factor relations between weighted and Nörlund means”, Tamkang J. Math., 50(1): 61-69, (2019).
13. 13. Sulaiman, W.T., “On some absolute summability factors of Infinite Series”, Gen. Math. Notes, 2, 2: 7-13, (2011).
14. 14. Hazar, G.C., Sarıgöl, M.A., “Absolute Cesàro series spaces and matrix operators”, Acta App. Math., 154: 153-165, (2018).
15. 15. Hazar Güleç, G.C., Sarıgöl, M.A., “Compact and Matrix Operators on the Space |𝐶, −1|𝑘”, J. Comput. Anal. Appl., 25(6): 1014-1024, (2018).
16. 16. Sarıgöl, M.A., “Spaces of series summable by absolute Cesàro and matrix operators”, Commun. Math. Appl., 7(1): 11-22, (2016).
17. 17. Sarıgöl, M.A., “Extension of Mazhar's theorem on summability factors”, Kuwait J. Sci.,42(3): 28-35, (2015).
18. 18. Maddox, I.J., “Elements of Functional Analysis”, Cambridge University Press, London, New York, (1970).