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Computation of matrix operators bounds with applying new extension of hardy inequality on weighted sequence spaces I

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Abstract

Themain goal of the present study is to give some estimations for upper bound and lower bound of some matrix operators on weighted sequence spaces d(w, p) and l p (w). We considered this problem for certain matrix operators such as Nörlund, Weighted mean, Ceasàro and Copson matrices, which is recently considered in [7–13]. Also, this study is an extension of [2]. Moreover, we present the exact solution of the lower and upper estimates for some particular matrix operators.

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References

  1. G. Bennett, Inequalities complimentary to Hardy, Quart. J. Math. Oxford(2) 49, 395 (1998).

    Article  MATH  Google Scholar 

  2. Chang-Pao Chen, Dah-Chin Luor, and Zong-Yin Ou, Extension of Hardy inequality, J. Math. Appl. 237, 160 (2002).

    MathSciNet  Google Scholar 

  3. D. Foroutannia and R. Lashkaripour, Lower bounds for summability matrices on weighted sequence spaces, Lobachevskii Journal of Mathematics 27, 15 (2007).

    MATH  MathSciNet  Google Scholar 

  4. G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic, Acta Math. 54, 81 (1930).

    Article  MathSciNet  Google Scholar 

  5. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, 2nd edition, (Cambridge University press, Cambridge 2001).

    Google Scholar 

  6. G. J. O. Jameson, Norms and lower bounds of operators on the Lorentz sequence space d(w, 1), Illinois J. Math. 43, 79 (1999).

    MATH  MathSciNet  Google Scholar 

  7. G. J. O. Jameson and R. Lashkaripour, Norms of certain operators on weighted l p spaces and Lorentz sequence spaces, J. Inequalities in Pure and Applied Mathematics 3(1), 6 (2002).

    MathSciNet  Google Scholar 

  8. R. Lashkaripour, Weighted Mean Matrix on Weighted Sequence Spaces, WSEAS Transaction on Mathematics 3(4), 789 (2004).

    MathSciNet  Google Scholar 

  9. R. Lashkaripour, Transpose of the Weighted Mean Operators on Weighted Sequence Spaces, WSEAS Transaction on Mathematics 4(4), 380 (2005).

    MathSciNet  Google Scholar 

  10. R. Lashkaripour and D. Foroutannia, Inequalities involving upper bounds for certain matrix operators, Proc. Indian Acad. Sci. (Math. Sci.) 116, 325 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  11. R. Lashkaripour and D. Foroutannia, Some inequalities involving upper bounds for some matrix operators I, Czechoslovak Mathematical Journal 57(132), 553 (2007).

    Article  MathSciNet  Google Scholar 

  12. R. Lashkaripour and D. Foroutannia, Lower Bounds for Matrices on Weighted Sequence Spaces, Journal of Sciences, Islamic Republic of Iran 18(1), 49 (2007).

    MathSciNet  Google Scholar 

  13. J. Pecaric, I. Peric, R. Roki, On bounds for weighted norms for matrices and integral operators, Linear Algebra and Appl. 326, 121 (2001).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dept. of Math., University of Sistan and Baluchestan Zahedan, Zahedan, Iran

    R. Lashkaripour & D. Foroutannia

Authors
  1. R. Lashkaripour
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  2. D. Foroutannia
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Correspondence to R. Lashkaripour.

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(Submitted by O.E. Tikhonov)

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Lashkaripour, R., Foroutannia, D. Computation of matrix operators bounds with applying new extension of hardy inequality on weighted sequence spaces I. Lobachevskii J Math 30, 40–45 (2009). https://doi.org/10.1134/S1995080209010065

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  • DOI: https://doi.org/10.1134/S1995080209010065

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