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Handbook of Functional Equations pp 147–160Cite as

Comparisons of Means and Related Functional Inequalities

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

Abstract

We provide a survey of several results on functional inequalities stemming from inequalities between classical means. Further, we recall a few problems in this field which according to the best of author’s knowledge remain open. Last section of this paper is devoted to a new, more general functional inequality and a joint generalization of several earlier results is obtained.

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Acknowledgements

The research of the author was supported by the Polish Ministry of Science and Higher Education in the years 2013–2014, under Project No. IP2012 011072.

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  1. Institute of Mathematics, University of Silesia, Bankowa 14, 40–007, Katowice, Poland

    Włodzimierz Fechner

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  1. Włodzimierz Fechner
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Correspondence to Włodzimierz Fechner .

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

    Themistocles M. Rassias

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Fechner, W. (2014). Comparisons of Means and Related Functional Inequalities. 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_8

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