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Continuous Forms of Classical Inequalities

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Abstract

The main aim of this paper is to focus on the question to develop classical inequalities to hold in a more general “continuous” form (involving infinitely many functions and/or spaces). First, we discuss such developments concerning Hölder’s and Minkowski’s inequalities. After that we present such new general developments of Popoviciu’s and Bellman’s inequalities. Finally, we present some applications, possible extensions and questions for further research.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Sofia University, Sofia, Bulgaria

    Ludmila Nikolova

  2. Luleå University of Technology, Luleå, Sweden

    Lars-Erik Persson

  3. UiT, The Artic University of Norway, Narvik, Norway

    Lars-Erik Persson

  4. Department of Mathematics, University of Zagreb, Zagreb, Croatia

    Sanja Varošanec

Authors
  1. Ludmila Nikolova
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  2. Lars-Erik Persson
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  3. Sanja Varošanec
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Corresponding author

Correspondence to Sanja Varošanec.

Additional information

The research of Ludmila Nikolova was partially supported by the Sofia University SRF under contract No 146/2015. The research of Sanja Varošanec was supported by Croatian Science Foundation under the project 5435.

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Nikolova, L., Persson, LE. & Varošanec, S. Continuous Forms of Classical Inequalities. Mediterr. J. Math. 13, 3483–3497 (2016). https://doi.org/10.1007/s00009-016-0698-4

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  • DOI: https://doi.org/10.1007/s00009-016-0698-4

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