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Supermeasures Associated to Some Classical Inequalities

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Abstract

In this paper we give some examples of supermeasures that are naturally associated to classical inequalities such as Jensen’s inequality, Hölder’s inequality, Minkowski’s inequality, Cauchy–Bunyakovsky–Schwarz’s inequality, Čebyšev’s inequality, Hermite–Hadamard’s inequalities and the definition of convexity property. As a consequence of monotonic nondecreasing property of these supermeasures, some refinements of the above inequalities are also obtained.

In Honor of Constantin Carathéodory

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Author information

Authors and Affiliations

  1. Department of Mathematics, College of Engineering and Science, Victoria University, Melbourne, VIC, Australia

    Silvestru Sever Dragomir

  2. School of Computer Science and Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa

    Silvestru Sever Dragomir

Authors
  1. Silvestru Sever Dragomir
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Correspondence to Silvestru Sever Dragomir .

Editor information

Editors and Affiliations

  1. Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Mathematics, National Technical Unversity of Athens Department of Mathematics, Athens, Greece

    Themistocles M. Rassias

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Dragomir, S.S. (2016). Supermeasures Associated to Some Classical Inequalities. In: Pardalos, P., Rassias, T. (eds) Contributions in Mathematics and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-31317-7_8

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