On a problem of Matkowski

• Autorzy: Zoltán Daróczy , Gyula Maksa
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

functional equation; quasi-arithmetic mean; convexity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 82
• Numer: 1
• Strony: 117-123

Daty

wydano

1999

otrzymano

1999-04-13

poprawiono

1999-05-17

Twórcy

autor

Zoltán Daróczy

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

autor

Gyula Maksa

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

Bibliografia

• [1] J. Aczél, Lectures on Functional Equations and Their Applications, Academic Press, New York, 1966.
• [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.