Taiwanese Journal of Mathematics

ON $q$-HAUSDORFF MATRICES

T. Selmanogullari, E. Savaş, and B. E. Rhoades

Full-text: Open access

Abstract

The q-Hausdorff matrices are defined in terms of symbols from q-mathematics. The matrices become ordinary Hausdorrf matrices as $q \rightarrow 1$. In this paper, we consider the q-analogues of the Cesàro matrix of order one, both for $0 \lt q \lt 1$ and $q \gt 1$, and obtain the lower bounds for these matrices for any $1 \lt p \lt \infty$.

Article information

Source
Taiwanese J. Math., Volume 15, Number 6 (2011), 2429-2437.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406479

Digital Object Identifier
doi:10.11650/twjm/1500406479

Mathematical Reviews number (MathSciNet)
MR2896126

Zentralblatt MATH identifier
1268.40005

Subjects
Primary: 40C05: Matrix methods
Secondary: 40G05: Cesàro, Euler, Nörlund and Hausdorff methods

Keywords
$q$-Hausdorff matrices lower bound problem $q$-Cesàro matrices

Citation

Selmanogullari, T.; Savaş, E.; Rhoades, B. E. ON $q$-HAUSDORFF MATRICES. Taiwanese J. Math. 15 (2011), no. 6, 2429--2437. doi:10.11650/twjm/1500406479. https://projecteuclid.org/euclid.twjm/1500406479


Export citation

References

  • G. Bennett, Lower bounds for matrices, Linear Algebra and Its Applications, 82 (1986), 81-98.
  • G. Bennett, Lower bounds for matrices. II, Canad. J. Math., 44(1) (1992), 54-74.
  • G. Bennett, An inequality for Hausdorff means, Houston J. Math., 25(4) (1999), 709-744.
  • J. Bustoz and L. F. Gordillo, q-Hausdorff Summability, J. Comput. Anal. Appl., 7(1) (2005), 35-48.
  • G. H. Hardy, Divergent Series, Oxford University Press, 1949.
  • F. Hausdorff, Summation methoden und Momentfolgen, I, Math. Z., 9 (1921), 74-109.
  • W. A. Hurwitz and L. L. Silverman, On the consistency and equivalence of certain definitions of summability, Trans. Amer. Math. Soc., 18 (1917), 1-20.
  • R. Lyons, A lower bound on the Cesaro operator, Proc. Amer. Math. Society, 86(4) (1982), 694.
  • B. E. Rhoades, Lower bounds for some matrices II, Linear and Multilinear Algebra, 26(1-2) (1990), 49-58.
  • B. E. Rhoades and Pali Sen, Lower bounds for some factorable matrices, Int. J. Math. Math. Sci., 2006, Art. ID 76135, 13 pp.
  • B. E. Rhoades and Pali Sen, Erratum: Lower bounds for some factorable matrices, [Int. J. Math. and Math. Sci., (2006), ID 76135, 13 pp.; MR2251755], Int. J. Math. Math. Sci. 2007, Art. ID 29096, 3 pp.
  • G. O. Thorin, An extension of a convexity theorem due to, M. Riesz, Kungl, Fysiograf\ilz ska Sallskapets i Lund Fordhandinger, 8 (1939), No. 14.