ArticleOriginal scientific text

Title

On a problem of Matkowski

Authors 1, 1

Affiliations

  1. Institute of Mathematics and Informatics, Kossuth Lajos University, H-4010 Debrecen Pf. 12, Hungary

Abstract

We solve Matkowski's problem for strictly comparable quasi-arithmetic means.

Keywords

functional equation, quasi-arithmetic mean, convexity

Bibliography

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  2. Z. Daróczy, On a class of means of two variables, Publ. Math. Debrecen 55 (1999), 177-197.
  3. Z. Daróczy and Zs. Páles, On means that are both quasi-arithmetic and conjugate arithmetic, Acta Math. Hungar., submitted.
  4. G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press., Cambridge, 1934.
  5. M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Cauchy's Equation and Jensen's Inequality, Uniw. Śląski and PWN, Katowice-Kraków-Warszawa, 1985.
  6. J. Matkowski, Invariant and complementary quasi-arithmetic means, Aequationes Math. 57 (1999), 87-107.
  7. J. Matkowski, Complementary quasi-arithmetic means, in: Leaflets in Mathematics, Proc. Numbers, Functions, Equations '98 Internat. Conf. Noszvaj (Hungary), Pécs, 1998, 123-124.
  8. A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973.
Pages:
117-123
Main language of publication
English
Received
1999-04-13
Accepted
1999-05-17
Published
1999
Exact and natural sciences