A New Result on Generalized Absolute Cesàro Summability

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Hüseyin Bor, Ram N. Mohapatra, A New Result on Generalized Absolute Cesàro Summability, Int. J. Anal. Appl., 11 (1) (2016), 40-42.

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Hüseyin Bor, Ram N. Mohapatra

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.

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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 Cesà ro 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.