On Quasi-Power Increasing Sequences and Their Some Applications

Article Sidebar

PDF
Cite as:
Hüseyin Bor, On Quasi-Power Increasing Sequences and Their Some Applications, Int. J. Anal. Appl., 10 (2) (2016), 95-100.

Main Article Content

Hüseyin Bor

Abstract

In [6], we proved a main theorem dealing with |N,pn,θn |k summability factors using a new general class of power increasing sequences instead of a quasi-σ-power increasing sequence. In this paper, we prove that theorem under weaker conditions. This theorem also includes some new results.

Article Details

References

  1. H. Bor, On two summability methods, Math. Proc. Camb. Philos. Soc., 97 (1985), 147-149.
  2. H. Bor, On the relative strength of two absolute summability methods, Proc. Amer. Math. Soc., 113 (1991), 1009-1012.
  3. H. Bor, A general note on increasing sequences, JIPAM. J. Inequal. Pure Appl. Math., 8 (2007), Article ID 82.
  4. H. Bor, New application of power increasing sequences, Math. Aeterna, 2 (2012), 423-429.
  5. H. Bor, A new application of generalized power increasing sequences, Filomat, 26 (2012), 631-635.
  6. H. Bor, A new application of generalized quasi-power increasing sequences, Ukrainian Math. J., 64 (2012), 731-738.
  7. E. Cesà ro, Sur la multiplication des séries, Bull. Sci. Math., 14 (1890), 114-120.
  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. G. H. Hardy, Divergent Series, Oxford Univ. Press., Oxford, (1949).
  10. L. Leindler, A new application of quasi power increasing sequences, Publ. Math. Debrecen, 58 (2001), 791-796.
  11. K. N. Mishra and R. S. L. Srivastava, On | ¯ N,pn| summability factors of infinite series, Indian J. Pure Appl. Math., 15 (1984), 651-656.
  12. W. T. Sulaiman, On some summability factors of infinite series, Proc. Amer. Math. Soc., 115 (1992), 313-317.
  13. W. T. Sulaiman, Extension on absolute summability factors of infinite series, J. Math. Anal. Appl., 322 (2006), 1224-1230.
  14. W. T. Sulaiman, A note on |A|ksummability factors of infinite series, Appl. Math. Comput., 216 (2010), 2645-2648.