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A new result for weighted arithmetic mean summability factors of infinite series involving almost increasing sequences

Year 2019, Volume: 68 Issue: 2, 1611 - 1620, 01.08.2019
https://doi.org/10.31801/cfsuasmas.546583

Abstract

In this paper, a known theorem dealing with weighted mean summability methods of non-decreasing sequences has been generalized for |A,p_{n};δ|_{k} summability factors of almost increasing sequences. Also, some new results have been obtained concerning |N,p_{n}|_{k}, |N,p_{n};δ|_{k} and |C,1;δ|_{k} summability factors.

References

  • Bari, N.K. and Stechkin, S.B., Best approximation and differential properties of two conjugate functions, Tr. Mosk. Mat. Obshch., vol. 5 (1956), 483-522.
  • Braha, N. L., Some weighted equi-statistical convergence and Korovkin type- theorem, Res. Math., 70(34) (2014), 433-446.
  • Bor, H., On two summability methods, Math. Proc. Camb. Philos. Soc., 97 (1985), 147-149.
  • Bor, H., A note on |N,p_{n}|_{k} summability factors of infinite series, Indian J. Pure Appl. Math., 18 (1987), 330-336.
  • Bor, H., On local property of |N,p_{n};δ|_{k} summability of factored Fourier series, J. Math. Anal. Appl., 179 (1993), 646-649.
  • Bor, H., A study on absolute Riesz summability factors, Rend. Circ. Mat. Palermo (2), 56 (2007) 358-368.
  • Bor, H., Factors for absolute weighted arithmetic mean summability of infinite series, Int. J. Anal. and Appl., 14 (2) (2017), 175-179.
  • Bor, H., On some new results for non-decreasing sequences, Tbilisi Math. J., 10 (2), (2017), 57-64.
  • Cesàro, E., Sur la multension of absolute summability and some theorems of Littlewood and Paley, Proc. Lond. Math. Soc., 7 (1957), 113-141.
  • Flett, T. M., Some more theorems concerning the absolute summability of Fourier series and power series, Proc.London Math. Soc., 8 (1958), 357-387.
  • Hardy, G. H., Divergeiplication des séries, Bull. Sci. Math., 14 (1890), 114-120.
  • Flett, T. M., On an extnt Series, Clarendon Press, Oxford 1949.
  • Mishra, K. N., On the absolute Nörlund summability factors of infinite series, Indian J. Pure Appl. Math., 14 (1983), 40-43.
  • Mishra, K. N. and Srivastava, R. S. L., On the absolute Cesaro summability factors of infinite series, Portugal Math., 42 (1983/84), 53-61.
  • Mishra, K. N. and Srivastava, R. S. L., On |N,p_{n}| summability factors of infinite series, Indian J. Pure Appl. Math.,15 (1984), 651-656.
  • Özarslan, H. S. and Öğdük, H. N., Generalizations of two theorems on absolute summability methods, Aust. J. Math. Anal. Appl. 13 (2004), 7pp.
  • Powell, R. E. and Shah, S. M., Summability theory and its applications, Van Nostrand, London, 1972.
  • Sezer, S. A. and Canak, I., Tauberian remainder theorems for the weighted mean method of summability, Math. Model. Anal., 19(2) (2014), 275-280.
  • Sezer, S. A. and Canak, I., On a Tauberian theorem for the weighted mean method of summability, Kuwait J. Sci., 42(3) (2015), 1-9.
  • Sulaiman, W. T, Inclusion theorems for absolute matrix summability methods of an infinite series, Indian J. Pure Appl. Math. 34 (11) (2003), 1547-1557.
  • Yildiz, Ş. A matrix application on absolute weighted arithmetic mean summability factors of infinite series, Tibilisi Math.J., (11) 2 (2018), 59-65.
  • Yildiz, Ş. A new result on weighted arithmetic mean summability of almost increasing sequences, 2nd International Conference of Mathematical Sciences (ICMS 2018), Maltepe University,31 July 2018-6 August 2018.
Year 2019, Volume: 68 Issue: 2, 1611 - 1620, 01.08.2019
https://doi.org/10.31801/cfsuasmas.546583

Abstract

References

  • Bari, N.K. and Stechkin, S.B., Best approximation and differential properties of two conjugate functions, Tr. Mosk. Mat. Obshch., vol. 5 (1956), 483-522.
  • Braha, N. L., Some weighted equi-statistical convergence and Korovkin type- theorem, Res. Math., 70(34) (2014), 433-446.
  • Bor, H., On two summability methods, Math. Proc. Camb. Philos. Soc., 97 (1985), 147-149.
  • Bor, H., A note on |N,p_{n}|_{k} summability factors of infinite series, Indian J. Pure Appl. Math., 18 (1987), 330-336.
  • Bor, H., On local property of |N,p_{n};δ|_{k} summability of factored Fourier series, J. Math. Anal. Appl., 179 (1993), 646-649.
  • Bor, H., A study on absolute Riesz summability factors, Rend. Circ. Mat. Palermo (2), 56 (2007) 358-368.
  • Bor, H., Factors for absolute weighted arithmetic mean summability of infinite series, Int. J. Anal. and Appl., 14 (2) (2017), 175-179.
  • Bor, H., On some new results for non-decreasing sequences, Tbilisi Math. J., 10 (2), (2017), 57-64.
  • Cesàro, E., Sur la multension of absolute summability and some theorems of Littlewood and Paley, Proc. Lond. Math. Soc., 7 (1957), 113-141.
  • Flett, T. M., Some more theorems concerning the absolute summability of Fourier series and power series, Proc.London Math. Soc., 8 (1958), 357-387.
  • Hardy, G. H., Divergeiplication des séries, Bull. Sci. Math., 14 (1890), 114-120.
  • Flett, T. M., On an extnt Series, Clarendon Press, Oxford 1949.
  • Mishra, K. N., On the absolute Nörlund summability factors of infinite series, Indian J. Pure Appl. Math., 14 (1983), 40-43.
  • Mishra, K. N. and Srivastava, R. S. L., On the absolute Cesaro summability factors of infinite series, Portugal Math., 42 (1983/84), 53-61.
  • Mishra, K. N. and Srivastava, R. S. L., On |N,p_{n}| summability factors of infinite series, Indian J. Pure Appl. Math.,15 (1984), 651-656.
  • Özarslan, H. S. and Öğdük, H. N., Generalizations of two theorems on absolute summability methods, Aust. J. Math. Anal. Appl. 13 (2004), 7pp.
  • Powell, R. E. and Shah, S. M., Summability theory and its applications, Van Nostrand, London, 1972.
  • Sezer, S. A. and Canak, I., Tauberian remainder theorems for the weighted mean method of summability, Math. Model. Anal., 19(2) (2014), 275-280.
  • Sezer, S. A. and Canak, I., On a Tauberian theorem for the weighted mean method of summability, Kuwait J. Sci., 42(3) (2015), 1-9.
  • Sulaiman, W. T, Inclusion theorems for absolute matrix summability methods of an infinite series, Indian J. Pure Appl. Math. 34 (11) (2003), 1547-1557.
  • Yildiz, Ş. A matrix application on absolute weighted arithmetic mean summability factors of infinite series, Tibilisi Math.J., (11) 2 (2018), 59-65.
  • Yildiz, Ş. A new result on weighted arithmetic mean summability of almost increasing sequences, 2nd International Conference of Mathematical Sciences (ICMS 2018), Maltepe University,31 July 2018-6 August 2018.
There are 22 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Şebnem Yıldız

Publication Date August 1, 2019
Submission Date July 31, 2018
Acceptance Date January 15, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Yıldız, Ş. (2019). A new result for weighted arithmetic mean summability factors of infinite series involving almost increasing sequences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1611-1620. https://doi.org/10.31801/cfsuasmas.546583
AMA Yıldız Ş. A new result for weighted arithmetic mean summability factors of infinite series involving almost increasing sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1611-1620. doi:10.31801/cfsuasmas.546583
Chicago Yıldız, Şebnem. “A New Result for Weighted Arithmetic Mean Summability Factors of Infinite Series Involving Almost Increasing Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1611-20. https://doi.org/10.31801/cfsuasmas.546583.
EndNote Yıldız Ş (August 1, 2019) A new result for weighted arithmetic mean summability factors of infinite series involving almost increasing sequences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1611–1620.
IEEE Ş. Yıldız, “A new result for weighted arithmetic mean summability factors of infinite series involving almost increasing sequences”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1611–1620, 2019, doi: 10.31801/cfsuasmas.546583.
ISNAD Yıldız, Şebnem. “A New Result for Weighted Arithmetic Mean Summability Factors of Infinite Series Involving Almost Increasing Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1611-1620. https://doi.org/10.31801/cfsuasmas.546583.
JAMA Yıldız Ş. A new result for weighted arithmetic mean summability factors of infinite series involving almost increasing sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1611–1620.
MLA Yıldız, Şebnem. “A New Result for Weighted Arithmetic Mean Summability Factors of Infinite Series Involving Almost Increasing Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1611-20, doi:10.31801/cfsuasmas.546583.
Vancouver Yıldız Ş. A new result for weighted arithmetic mean summability factors of infinite series involving almost increasing sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1611-20.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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