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An Introduction to Ultrametric Summability Theory pp 133–155Cite as

The Nörlund Method and The Weighted Mean Method for Double Sequences

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Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM,volume 2))

Abstract

In the current chapter, we introduce the Nörlund method and the Weighted Mean method for double sequences and establish many of their properties.

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References

  1. Natarajan, P.N., Srinivasan, V.: Silverman-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields. Ann. Math. Blaise Pascal 9, 85–100 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Natarajan, P.N., Sakthivel, S.:Multiplication of double series and convolution of double infinite matrices in non-archimedean fields. Indian J. Math. 50, 125–133 (2008)

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  3. Natarajan, P.N., Sakthivel, S.: Weighted means for double sequences in non-archimedean fields. Indian J. Math. 48, 201–220 (2006)

    MathSciNet  MATH  Google Scholar 

  4. Rangachari, M.S., Srinivasan, V.K.: Matrix transformations in non-archimedean fields. Indag. Math. 26, 422–429 (1964)

    Article  MathSciNet  Google Scholar 

  5. Katok, S.: \(p\)-adic analysis compared with real, Student Mathematical Library, Amer. Math. Soc. 37 (2007)

    Google Scholar 

  6. Natarajan, P.N., Rangachari, M.S.: Matrix transformations between sequence spaces over non-archimedean fields. Rev. Roum. Math. Pures Appl. 24, 615–618 (1979)

    MathSciNet  MATH  Google Scholar 

  7. Natarajan, P.N.: On a scale of summation processes in the \(p\)-adic field. Bull. Soc. Math. Belgique 31, 67–73 (1979)

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  8. Natarajan, P.N.: Continuous duals of certain sequence spaces and the related matrix transformations over non-archimedean fields. Indian J. Pure Appl. Math. 21, 82–87 (1990)

    MathSciNet  MATH  Google Scholar 

  9. Natarajan, P.N.: Characterization of some special classes of infinite matrices over non-archimedean fields. Indian J. Math. 34, 45–51 (1992)

    MathSciNet  MATH  Google Scholar 

  10. Natarajan, P.N.: Matrix transformations between certain sequences spaces over valued fields. Indian J. Math. 39, 177–182 (1997)

    MathSciNet  MATH  Google Scholar 

  11. Natarajan, P.N.: On the Algebras \((c, c)\) and (\(l_\alpha , l_\alpha \)) in Non-archimedean Fields. Lecture Notes in Pure and Applied Mathematics, pp. 225–231. Marcel Dekker, New York (1999)

    Google Scholar 

  12. Natarajan, P.N.: Matrix transformations between certain sequence spaces over valued fields II. Indian J. Math. 43, 353–358 (2001)

    MathSciNet  MATH  Google Scholar 

  13. Natarajan, P.N.: Some Properties of Certain Sequence Spaces Over Non-archimedean Fields, \(p\)-adic Functional Analysis. Lecture Notes in Pure and Applied Mathematics, pp. 227–232. Marcel Dekker, New York (2001)

    Google Scholar 

  14. Natarajan, P.N.: On the algebra \((c_0, c_0)\) of infinite matrices in non-archimedean fields. Indian J. Math. 45, 79–87 (2003)

    MathSciNet  MATH  Google Scholar 

  15. Natarajan, P.N.: Some results on certain summability methods in non-archimedean fields. J. Comb. Inf. Syst. Sci. 33, 151–161 (2008)

    MATH  Google Scholar 

  16. Natarajan, P.N.: Some more results on the Nörlund and \(Y\) methods of summability in non-archimedean fields. J. Comb. Inf. Syst. Sci. 35, 81–90 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Natarajan, P.N.: More properties of \(c_0(p)\) over non-archimedean fields. J. Comb. Inf. Syst. Sci. 38, 121–127 (2013)

    MATH  Google Scholar 

  18. Bhaskaran, R., Natarajan, P.N.: The space \(c_0(p)\) over valued fields. Rocky Mt. J. Math. 16, 129–136 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  19. Raghunathan, T.T.: On the space of entire functions over certain non-archimedean fields. Boll. Un. Mat. Ital. 1, 517–526 (1968)

    MathSciNet  MATH  Google Scholar 

  20. Raghunathan, T.T.: The space of entire functions over certain non-archimedean fields and its dual. Studia Math. 33, 251–256 (1969)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Formerly of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamil Nadu, India

    P. N. Natarajan

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  1. P. N. Natarajan
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Correspondence to P. N. Natarajan .

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Natarajan, P.N. (2015). The Nörlund Method and The Weighted Mean Method for Double Sequences. In: An Introduction to Ultrametric Summability Theory. Forum for Interdisciplinary Mathematics, vol 2. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2559-1_9

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