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A study on absolute summability factors

Year 2020, Volume: 24 Issue: 1, 220 - 223, 01.02.2020
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.

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.
Year 2020, Volume: 24 Issue: 1, 220 - 223, 01.02.2020
https://doi.org/10.16984/saufenbilder.642406

Abstract

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.
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

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

Publication Date February 1, 2020
Submission Date November 4, 2019
Acceptance Date December 12, 2019
Published in Issue Year 2020 Volume: 24 Issue: 1

Cite

APA Hazar Güleç, G. C. (2020). A study on absolute summability factors. Sakarya University Journal of Science, 24(1), 220-223. https://doi.org/10.16984/saufenbilder.642406
AMA Hazar Güleç GC. A study on absolute summability factors. SAUJS. February 2020;24(1):220-223. doi:10.16984/saufenbilder.642406
Chicago Hazar Güleç, G. Canan. “A Study on Absolute Summability Factors”. Sakarya University Journal of Science 24, no. 1 (February 2020): 220-23. https://doi.org/10.16984/saufenbilder.642406.
EndNote Hazar Güleç GC (February 1, 2020) A study on absolute summability factors. Sakarya University Journal of Science 24 1 220–223.
IEEE G. C. Hazar Güleç, “A study on absolute summability factors”, SAUJS, vol. 24, no. 1, pp. 220–223, 2020, doi: 10.16984/saufenbilder.642406.
ISNAD Hazar Güleç, G. Canan. “A Study on Absolute Summability Factors”. Sakarya University Journal of Science 24/1 (February 2020), 220-223. https://doi.org/10.16984/saufenbilder.642406.
JAMA Hazar Güleç GC. A study on absolute summability factors. SAUJS. 2020;24:220–223.
MLA Hazar Güleç, G. Canan. “A Study on Absolute Summability Factors”. Sakarya University Journal of Science, vol. 24, no. 1, 2020, pp. 220-3, doi:10.16984/saufenbilder.642406.
Vancouver Hazar Güleç GC. A study on absolute summability factors. SAUJS. 2020;24(1):220-3.