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On the properties of McShane’s functional and their applications

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Abstract

In this paper we derive some remarkable properties of McShane’s functional, defined by means of positive isotonic linear functionals. These properties are then applied to weighted generalized means. A series of consequences among additive and multiplicative type mean inequalities is given, as well as a special consideration of Hölder’s inequality, in view of the new results.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000, Zagreb, Croatia

    Mario Krnić

  2. Faculty of Civil Engineering and Architecture, University of Zagreb, Matice hrvatske 15, 21 000, Split, Croatia

    Neda Lovričević

  3. Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000, Zagreb, Croatia

    Josip Pečarić

Authors
  1. Mario Krnić
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  2. Neda Lovričević
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  3. Josip Pečarić
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Corresponding author

Correspondence to Mario Krnić.

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Communicated by László Hatvani

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Krnić, M., Lovričević, N. & Pečarić, J. On the properties of McShane’s functional and their applications. Period Math Hung 66, 159–180 (2013). https://doi.org/10.1007/s10998-013-3571-2

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  • DOI: https://doi.org/10.1007/s10998-013-3571-2

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