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Estimating the Hardy Constant of Nonconcave Homogeneous Quasideviation Means Cover

Estimating the Hardy Constant of Nonconcave Homogeneous Quasideviation Means

Open Access
|Feb 2024

References

  1. T. Carleman, Sur les fonctions quasi-analitiques, in: Conférences faites au cinquième Congrès des Mathématiciens scandinaves, Librairie Académique, Helsingfors, 1923, pp. 181–196.
  2. Z. Daróczy and Zs. Páles, On comparison of mean values, Publ. Math. Debrecen 29 (1982), no. 1–2, 107–115.
  3. J. Duncan and C.M. McGregor, Carleman’s inequality, Amer. Math. Monthly 110 (2003), no. 5, 424–431.
  4. G.H. Hardy, Note on a theorem of Hilbert, Math. Z. 6 (1920), no. 3–4, 314–317.
  5. K. Kedlaya, Proof of a mixed arithmetic-mean, geometric-mean inequality, Amer. Math. Monthly 101 (1994), no. 4, 355–357.
  6. K.S. Kedlaya, A weighted mixed-mean inequality, Amer. Math. Monthly 106 (1999), no. 4, 355–358.
  7. K. Knopp, Über Reihen mit positiven Gliedern, J. London Math. Soc. 3 (1928), no. 3, 205–211.
  8. A. Kufner, L. Maligranda, and L.-E. Persson, The Hardy Inequality: About Its History and Some Related Results, Vydavatelský servis, Praha, 2007.
  9. E. Landau, A note on a theorem concerning series of positive terms, J. London Math. Soc. 1 (1921), no. 1, 38–39.
  10. Zs. Páles, Characterization of quasideviation means, Acta Math. Acad. Sci. Hungar. 40 (1982), no. 3–4, 243–260.
  11. Zs. Páles, General inequalities for quasideviation means, Aequationes Math. 36 (1988), no. 1, 32–56.
  12. Zs. Páles, On homogeneous quasideviation means, Aequationes Math. 36 (1988), no. 2–3, 132–152.
  13. Zs. Páles and P. Pasteczka, Characterization of the Hardy property of means and the best Hardy constants, Math. Inequal. Appl. 19 (2016), no. 4, 1141–1158.
  14. Zs. Páles and P. Pasteczka, On the best Hardy constant for quasi-arithmetic means and homogeneous deviation means, Math. Inequal. Appl. 21 (2018), no. 2, 585–599.
  15. Zs. Páles and P. Pasteczka, On the homogenization of means, Acta Math. Hungar. 159 (2019), no. 2, 537–562.
  16. Zs. Páles and P. Pasteczka, On Hardy type inequalities for weighted quasideviation means, Math. Inequal. Appl. 23 (2020), no. 3, 971–990.
  17. Zs. Páles and P. Pasteczka, On the Jensen convex and Jensen concave envelopes of means, Arch. Math. (Basel) 116 (2021), no. 4, 423–432.
  18. Zs. Páles and P. Pasteczka, Estimating the Hardy constant of nonconcave Gini means, Math. Inequal. Appl. 26, (2023), no. 1, 195–203.
  19. P. Pasteczka, On the Hardy property of mixed means, Math. Inequal. Appl. 24 (2021), no. 3, 873–885.
  20. J.E. Pečarić and K.B. Stolarsky, Carleman’s inequality: history and new generalizations, Aequationes Math. 61 (2001), no. 1–2, 49–62.
DOI: https://doi.org/10.2478/amsil-2024-0004 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 78 - 92
Submitted on: Jul 21, 2023
Accepted on: Jan 24, 2024
Published on: Feb 15, 2024
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2024 Zsolt Páles, Paweł Pasteczka, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.