Advertisement

Acta Mathematica Hungarica

, Volume 139, Issue 1–2, pp 1–10 | Cite as

Determination of conjugate means by reducing to the generalized Matkowski–Sutô equation

  • Justyna JarczykEmail author
Article

Abstract

Given a weighted quasi-arithmetic mean L on an interval I we find all conjugate means derived from L which are weighted quasi-arithmetic, that is we determine all numbers p,q∈(0,1] and continuous strictly monotonic functions φ: I→ℝ such that the mean given by is weighted quasi-arithmetic. Some special cases of the problem were solved by Z. Daróczy, Zs. Páles, Gy. Maksa and J. Dascăl.

Key words and phrases

mean functional equation quasi-arithmetic mean conjugate mean 

Mathematics Subject Classification

26E60 39B22 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. Burai, A Matkowski–Sutô type equation, Publ. Math. Debrecen, 70 (2007), 233–247. MathSciNetzbMATHGoogle Scholar
  2. [2]
    Z. Daróczy, On the equality and comparison problem of a class of mean values, Aequat. Math., 81 (2011), 201–208. zbMATHCrossRefGoogle Scholar
  3. [3]
    Z. Daróczy and J. Dascăl, On the equality problem of conjugate means, Results Math., 58 (2010), 69–79. MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Z. Daróczy and Zs. Páles, On means that are both quasi–arihtmetic and conjugate arithmetic, Acta Math. Hungar., 90 (2001), 271–282. MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Z. Daróczy and Zs. Páles, On functional equations involving means, Publ. Math. Debrecen, 62 (2003), 363–377. MathSciNetzbMATHGoogle Scholar
  6. [6]
    Z. Daróczy and Zs. Páles, Generalized convexity and comparison of mean values, Acta Sci. Math. (Szeged), 71 (2005), 105–116. MathSciNetzbMATHGoogle Scholar
  7. [7]
    J. Jarczyk, Invariance in the class of weighted quasi-arithmetic means with continuous generators, Publ. Math. Debrecen, 71 (2007), 279–294. MathSciNetzbMATHGoogle Scholar
  8. [8]
    J. Jarczyk, Regularity theorem for a functional equation involving means, Publ. Math. Debrecen, 75 (2009), 123–135. MathSciNetzbMATHGoogle Scholar
  9. [9]
    J. Jarczyk, On an equation involving weighted quasi-arithmetic means, Acta Math. Hungar., 129 (2010), 96–111. MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    J. Jarczyk and J. Matkowski, Invariance in the class of weighted quasi-arithmetic means, Ann. Polon. Math., 88 (2006), 39–51. MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Gy. Maksa and Z. Páles, Remarks on a comparison of weighted quasi-arithmetic means, Colloq. Math., 120 (2010), 77–84. MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    J. Matkowski, Invariant and complementary quasi-arithmetic means, Aequat. Math., 57 (1999), 87–107. MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics, Computer Science and EconometricsUniversity of Zielona GóraZielona GóraPoland

Personalised recommendations