An invariance of geometric mean with respect to Lagrangian means |
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| Authors: | Dorota G?azowska Janusz Matkowski |
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| Institution: | Department of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Podgórna 50, PL-65512 Zielona Góra, Poland |
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| Abstract: | The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g. |
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| Keywords: | Mean Lagrangian mean Invariant mean Iterate Functional equation |
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