Advertisement

The Nörlund, Weighted Mean, and \((M, \lambda _{m,n})\) Methods for Double Sequences

  • P. N. Natarajan
Chapter

Abstract

In the context of the new definition of convergence of a double sequence and double series introduced in Chap.  5, we define the Nörlund, the Weighted Mean, and the \((M, \lambda _{m,n})\) or Natarajan methods for double sequences and double series and study some of their properties.

Keywords

The Nörlund method Consistent Inclusion Equivalence The Weighted Mean method Limitation theorem The \((M, \lambda _{m, n})\) or Natarajan method 

References

  1. 1.
    Natarajan, P.N.: Nörlund means for double sequences and double series (communicated for publication)Google Scholar
  2. 2.
    Moore, C.N.: On relationships between Nörlund means for double series. Proc. Amer. Math. Soc. 5, 957–963 (1954)MathSciNetMATHGoogle Scholar
  3. 3.
    Natarajan, P.N.: Weighted means for double sequences and double series. Indian J. Math. 58, 31–42 (2016)MathSciNetMATHGoogle Scholar
  4. 4.
    Natarajan, P.N.: An inclusion theorem for weighted mean methods for double sequences. Indian J. Math. (Supplement) Proceedings Sixth Dr. George Bachman Memorial Conference, 57, 39–42 (2015)Google Scholar
  5. 5.
    Natarajan, P.N.: Natarajan method of summability for double sequences and double series. An. Stiint. Univ. Al. I. Cuza Iasi Math. (N.S.) Tomul LXII, 2, 547–552 (2016)Google Scholar
  6. 6.
    Natarajan, P.N.: New properties of the Natarajan method of summability for double sequences. Int. J. Phys. Math. Sci. 6(3), 28–33 (2016)Google Scholar
  7. 7.
    Butzer, P.L., Nessel, R.J.: Fourier Analysis and Applications. Birkhauser, Basel (1971)MATHGoogle Scholar
  8. 8.
    Schipp, F., Wade, W.R., Simon, P., Pal, J.: Walsh Series: An Introduction to Dyadic Harmonic Analysis. Adam Hilger, Bristol (1990)MATHGoogle Scholar
  9. 9.
    Shawyer, B., Watson, B.: Borel’s Methods of Summability. Oxford (1994)Google Scholar
  10. 10.
    Weisz, F.: Summability of Multidimensional Fourier series and Hardy spaces. Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht (2002)CrossRefMATHGoogle Scholar
  11. 11.
    Zygmund, A.: Trigonometric Series, 3rd edn. Cambridge, London (2002)MATHGoogle Scholar
  12. 12.
    Grafakos, L.: Classical and Modern Fourier Analysis. Pearson Education, New Jersey (2004)MATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Formerly of the Department of MathematicsRamakrishna Mission Vivekananda CollegeChennaiIndia

Personalised recommendations