Abstract
A functional equation that characterizes generalized Beckenbach-Gini means which are invariant with respect to Beckenbach-Gini mean-type mappings is considered. In the case when an invariant mean is either arithmetic or geometric or harmonic, without any regularity conditions, all solutions are found. In the general case, under some regularity assumptions, a necceasary condition is given. For positively homogeneous Beckenbach-Gini means a complete list of solutions is established. Translative Beckenbach-Gini means are also examined.
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Dedicated to Professor Peter Kahlig on the occasion of his sixtieth birthday
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© 2002 Springer Science+Business Media Dordrecht
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Matkowski, J. (2002). On Invariant Generalized Beckenbach-Gini Means. In: Daróczy, Z., Páles, Z. (eds) Functional Equations — Results and Advances. Advances in Mathematics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5288-5_17
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DOI: https://doi.org/10.1007/978-1-4757-5288-5_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5210-3
Online ISBN: 978-1-4757-5288-5
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