International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

A New Result on Generalized Absolute Cesàro Summability

  • Hüseyin Bor*
  • Ram N. Mohapatra

    * Corresponding author

    Abstract

    In [4], a main theorem dealing with an application of almost increasing sequences, has been proved. In this paper, we have extended that theorem by using a general class of quasi power increasing sequences, which is a wider class of sequences, instead of an almost increasing sequence. This theorem also includes some new and known results.

    How to Cite

    H. Bor, R. N. Mohapatra, A New Result on Generalized Absolute Cesàro Summability, Int. J. Anal. Appl. 11 (2016), 40–42.

    BibTeX
    @article{Bor2016,
      author  = {Bor, Hüseyin and Mohapatra, Ram N.},
      title   = {A New Result on Generalized Absolute Cesàro Summability},
      journal = {Int. J. Anal. Appl.},
      volume  = {11},
      year    = {2016},
      pages   = {40--42},
      doi     = {}
    }

    References

    • [1] N. K. Bari and S. B. Steˇ ckin, Best approximation and differential properties of two conjugate functions, Trudy. Moskov. Mat. Obˇ sˇ c., 5 (1956), 483-522 (in Russian).
    • [2] R. P. Boas, Quasi positive sequences and trigonometric series, Proc. London Math. Soc., 14A (1965), 38-46.
    • [3] H. Bor, On a new application of power increasing sequences, Proc. Est. Acad. Sci., 57 (2008), 205-209.
    • [4] H. Bor, On generalized absolute Cesàro summability, An. S ¸tiint ¸. Univ. Al. I. Cuza Ia ¸si. Mat. (N.S.), LVII (2011), 323-328.
    • [5] H. Bor, On the quasi monotone and generalized power increasing sequences and their new applications, J. Classical Anal., 2 (2013), 139-144.
    • [6] D. Borwein, Theorems on some methods of summability, Quart. J. Math. Oxford Ser. (2), 9 (1958), 310-316.
    • [7] G. Das, A Tauberian theorem for absolute summability, Proc. Camb. Phil. Soc., 67 (1970), 321-326.
    • [8] T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc., 7 (1957), 113-141.
    • [9] L. Leindler, A new application of quasi power increasing sequences, Publ. Math. Debrecen, 58 (2001), 791-796.
    • [10] S. M. Mazhar, On generalized quasi-convex sequence and its applications, Indian J. Pure Appl. Math., 8 (1977), 784-790.
    • [11] W. T. Sulaiman, Extension on absolute summability factors of infinite series, J. Math. Anal. Appl., 322 (2006), 1224-1230.