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

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.

___

  • 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.