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Inequalities for Convex and Concave Functions and a New Concept of Majorization Intended for Two Pairs of Vectors

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Abstract

In this paper, some inequalities for convex and concave functions are demonstrated. A new concept of majorization is applied for two pairs of vectors. Instead of the standard approach based on one doubly stochastic matrix, here two matrices are employed: one is both row stochastic and column substochastic, while the other is both column stochastic and row superstochastic. An inequality of Hardy–Littlewood–Pólya–Karamata type is derived for a row stochastic–column substochastic matrix.

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Acknowledgements

The author wishes to thank an anonymous referee for his/her valuable suggestions and comments improving the previous version of the manuscript.

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  1. Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Akademicka 13, 20-950, Lublin, Poland

    Marek Niezgoda

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  1. Marek Niezgoda
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Correspondence to Marek Niezgoda.

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Niezgoda, M. Inequalities for Convex and Concave Functions and a New Concept of Majorization Intended for Two Pairs of Vectors. Results Math 75, 34 (2020). https://doi.org/10.1007/s00025-020-1161-1

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  • DOI: https://doi.org/10.1007/s00025-020-1161-1

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