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Some New Results on Absolute Summability Factors

Year 2020, Volume: 16 Issue: 1, 89 - 93, 27.03.2020

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

References

  • 1. Sulaiman, W.T., “On some summability factors of infinite series”, Proc. Amer. Math. Soc., 115: 313-317, (1992).
  • 2. Bor, H., “On two summability methods”, Math. Proc. Cambridge Philos Soc., 97: 147-149, (1985).
  • 3. Sarıgöl, M.A., “On two absolute Riesz summability factors of infinite series” Proc. Amer. Math. Soc.,118: 485-488, (1993).
  • 4. Sarıgöl, M. A., “ On absolute factorable matrix summability methods” , Bull. Math. Anal. Appl., 8: 1-5, (2016).
  • 5. Borwein, D., “Theorems on some methods of summability”, Quart. J. Math. Oxford Ser. (2), 9: 310-314, (1958).
  • 6. Das, G., “A Tauberian theorem for absolute summability”, Proc. Camb. Phil. Soc., 67: 321-326, (1970).
  • 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. Mazhar, S.M. “On the absolute summability factors of infinite series”, Tohoku Math. J., 23: 433-451, (1971).
  • 9. Mehdi, M.R., “Summability factors for generalized absolute summability I”, Proc. London Math. Soc., 10(3): 180-199, (1960).
  • 10. Mohapatra, R.N., “On absolute Riesz summability factors”, J. Indian Math. Soc., 32: 113-129, (1968).
  • 11. Bor, H., “Some equivalence theorems on absolute summability methods”, Acta Math. Hung., 149: 208-214, (2016).
  • 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. Sulaiman, W.T., “On some absolute summability factors of Infinite Series”, Gen. Math. Notes, 2, 2: 7-13, (2011).
  • 14. Hazar, G.C., Sarıgöl, M.A., “Absolute Cesàro series spaces and matrix operators”, Acta App. Math., 154: 153-165, (2018).
  • 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. Sarıgöl, M.A., “Spaces of series summable by absolute Cesàro and matrix operators”, Commun. Math. Appl., 7(1): 11-22, (2016).
  • 17. Sarıgöl, M.A., “Extension of Mazhar's theorem on summability factors”, Kuwait J. Sci.,42(3): 28-35, (2015).
  • 18. Maddox, I.J., “Elements of Functional Analysis”, Cambridge University Press, London, New York, (1970).
Year 2020, Volume: 16 Issue: 1, 89 - 93, 27.03.2020

Abstract

References

  • 1. Sulaiman, W.T., “On some summability factors of infinite series”, Proc. Amer. Math. Soc., 115: 313-317, (1992).
  • 2. Bor, H., “On two summability methods”, Math. Proc. Cambridge Philos Soc., 97: 147-149, (1985).
  • 3. Sarıgöl, M.A., “On two absolute Riesz summability factors of infinite series” Proc. Amer. Math. Soc.,118: 485-488, (1993).
  • 4. Sarıgöl, M. A., “ On absolute factorable matrix summability methods” , Bull. Math. Anal. Appl., 8: 1-5, (2016).
  • 5. Borwein, D., “Theorems on some methods of summability”, Quart. J. Math. Oxford Ser. (2), 9: 310-314, (1958).
  • 6. Das, G., “A Tauberian theorem for absolute summability”, Proc. Camb. Phil. Soc., 67: 321-326, (1970).
  • 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. Mazhar, S.M. “On the absolute summability factors of infinite series”, Tohoku Math. J., 23: 433-451, (1971).
  • 9. Mehdi, M.R., “Summability factors for generalized absolute summability I”, Proc. London Math. Soc., 10(3): 180-199, (1960).
  • 10. Mohapatra, R.N., “On absolute Riesz summability factors”, J. Indian Math. Soc., 32: 113-129, (1968).
  • 11. Bor, H., “Some equivalence theorems on absolute summability methods”, Acta Math. Hung., 149: 208-214, (2016).
  • 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. Sulaiman, W.T., “On some absolute summability factors of Infinite Series”, Gen. Math. Notes, 2, 2: 7-13, (2011).
  • 14. Hazar, G.C., Sarıgöl, M.A., “Absolute Cesàro series spaces and matrix operators”, Acta App. Math., 154: 153-165, (2018).
  • 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. Sarıgöl, M.A., “Spaces of series summable by absolute Cesàro and matrix operators”, Commun. Math. Appl., 7(1): 11-22, (2016).
  • 17. Sarıgöl, M.A., “Extension of Mazhar's theorem on summability factors”, Kuwait J. Sci.,42(3): 28-35, (2015).
  • 18. Maddox, I.J., “Elements of Functional Analysis”, Cambridge University Press, London, New York, (1970).
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

G. Canan Hazar Güleç 0000-0002-8825-5555

Publication Date March 27, 2020
Published in Issue Year 2020 Volume: 16 Issue: 1

Cite

APA Hazar Güleç, G. C. (2020). Some New Results on Absolute Summability Factors. Celal Bayar University Journal of Science, 16(1), 89-93.
AMA Hazar Güleç GC. Some New Results on Absolute Summability Factors. CBUJOS. March 2020;16(1):89-93.
Chicago Hazar Güleç, G. Canan. “Some New Results on Absolute Summability Factors”. Celal Bayar University Journal of Science 16, no. 1 (March 2020): 89-93.
EndNote Hazar Güleç GC (March 1, 2020) Some New Results on Absolute Summability Factors. Celal Bayar University Journal of Science 16 1 89–93.
IEEE G. C. Hazar Güleç, “Some New Results on Absolute Summability Factors”, CBUJOS, vol. 16, no. 1, pp. 89–93, 2020.
ISNAD Hazar Güleç, G. Canan. “Some New Results on Absolute Summability Factors”. Celal Bayar University Journal of Science 16/1 (March 2020), 89-93.
JAMA Hazar Güleç GC. Some New Results on Absolute Summability Factors. CBUJOS. 2020;16:89–93.
MLA Hazar Güleç, G. Canan. “Some New Results on Absolute Summability Factors”. Celal Bayar University Journal of Science, vol. 16, no. 1, 2020, pp. 89-93.
Vancouver Hazar Güleç GC. Some New Results on Absolute Summability Factors. CBUJOS. 2020;16(1):89-93.