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Invariance in the Family of Weighted Gini Means

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Handbook of Functional Equations

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 95))

Abstract

Given two means M and N, the mean P is called \((M,N)\)-invariant if \(P(M,\) \(N)=P.\) At the same time the mean N is called complementary to M with respect to P. We use the method of series expansion of means to determine the complementary with respect to a weighted Gini mean. The invariance in the family of weighted Gini means is also studied. The computer algebra Maple was used for solving some complicated systems of equations.

Mathematics subject classification(2000): 26E60

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Authors and Affiliations

  1. Technical University Cluj-Napoca, 28 Memorandumului Street, 400114, Cluj-Napoca, Romania

    Iulia Costin & Gheorghe Toader

Authors
  1. Iulia Costin
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  2. Gheorghe Toader
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Correspondence to Iulia Costin .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Costin, I., Toader, G. (2014). Invariance in the Family of Weighted Gini Means. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1246-9_6

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