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Functional equations involving means

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Abstract

In this paper, the functional equation

$$ f(px + (1 - p)y) + f((1 - p)x + py) = f(x) + f(y), (x,y \in I) $$

is considered, where 0 < p < 1 is a fixed parameter and f: I → R is an unknown function. The equivalence of this and Jensen’s functional equation is completely characterized in terms of the algebraic properties of the parameter p. As an application, solutions of certain functional equations involving four weighted arithmetic means are also determined.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, H-4010, Debrecen, Pf. 12, Hungary

    Z. Daróczy, K. Lajkó, R. L. Lovas, Gy. Maksa & Zs. Páles

Authors
  1. Z. Daróczy
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  2. K. Lajkó
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  3. R. L. Lovas
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  4. Gy. Maksa
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  5. Zs. Páles
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Additional information

This research was partly supported by the Hungarian Scientific Research Fund (OTKA) Grants T-043080, K 62316, and T-047373.

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Daróczy, Z., Lajkó, K., Lovas, R.L. et al. Functional equations involving means. Acta Math Hung 116, 79–87 (2007). https://doi.org/10.1007/s10474-007-5296-2

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  • DOI: https://doi.org/10.1007/s10474-007-5296-2

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