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The Hardy–Littlewood–Pólya inequality of majorization in the context of \(\mathbf {\omega }\)–\(\textbf{m}\)–star-convex functions

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Abstract

The Hardy–Littlewood–Pólya inequality of majorization is extended for \(\mathbf {\omega }\)–\(\textbf{m}\)–star-convex functions to the framework of ordered Banach spaces. Several open problems which seem to be of interest for further extensions of the Hardy–Littlewood–Pólya inequality are also included.

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Acknowledgements

The work of G. M. Lachescu and I. Roventa have been supported by a grant of the Romanian Ministry of Research, Innovation and Digitalization (MCID), project number 22 - Nonlinear Differential Systems in Applied Sciences, within PNRR-III-C9-2022-I8.

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  1. Department of Mathematics, University of Craiova, A.I. Cuza Street 13, Craiova, 200585, Romania

    Geanina Maria Lăchescu & Ionel Rovenţa

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  1. Geanina Maria Lăchescu
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  2. Ionel Rovenţa
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Yongge Tian wrote the main manuscript text.

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Correspondence to Ionel Rovenţa.

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Lăchescu, G.M., Rovenţa, I. The Hardy–Littlewood–Pólya inequality of majorization in the context of \(\mathbf {\omega }\)–\(\textbf{m}\)–star-convex functions. Aequat. Math. 97, 523–535 (2023). https://doi.org/10.1007/s00010-023-00942-5

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