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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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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DOI: https://doi.org/10.1007/978-3-319-31317-7_8
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