# On a problem of Matkowski

Colloquium Mathematicae (1999)

- Volume: 82, Issue: 1, page 117-123
- ISSN: 0010-1354

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topDaróczy, Zoltán, and Maksa, Gyula. "On a problem of Matkowski." Colloquium Mathematicae 82.1 (1999): 117-123. <http://eudml.org/doc/210744>.

@article{Daróczy1999,

abstract = {We solve Matkowski's problem for strictly comparable quasi-arithmetic means.},

author = {Daróczy, Zoltán, Maksa, Gyula},

journal = {Colloquium Mathematicae},

keywords = {functional equation; quasi-arithmetic mean; convexity; continuous strictly monotonic functions; functional equations},

language = {eng},

number = {1},

pages = {117-123},

title = {On a problem of Matkowski},

url = {http://eudml.org/doc/210744},

volume = {82},

year = {1999},

}

TY - JOUR

AU - Daróczy, Zoltán

AU - Maksa, Gyula

TI - On a problem of Matkowski

JO - Colloquium Mathematicae

PY - 1999

VL - 82

IS - 1

SP - 117

EP - 123

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

LA - eng

KW - functional equation; quasi-arithmetic mean; convexity; continuous strictly monotonic functions; functional equations

UR - http://eudml.org/doc/210744

ER -

## References

top- [1] J. Aczél, Lectures on Functional Equations and Their Applications, Academic Press, New York, 1966. Zbl0139.09301
- [2] Z. Daróczy, On a class of means of two variables, Publ. Math. Debrecen 55 (1999), 177-197. Zbl0932.39019
- [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. Zbl0930.26014
- [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. Zbl0271.26009

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