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Extended power difference means

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Abstract

The extended power difference mean \(f_{a,b}(t):={b\over a}{{t^a-1}\over {t^b-1}}\) \((a,b\in {\mathbb {R}})\) is investigated in this paper. We show some Thompson metric inequalities involving \(f_{a,b}\) and Tsallis relative operator entropy. We also discuss the behavior of the bivariate function defined as the perspective map for \(f_{a,b}\). Finally, the relationship beween \(f_{a,b}\) and the weighted logarithmic mean is studied.

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Acknowledgements

I would like to thank Fumio Hiai for his many helpful suggestions in the preparation of this paper.

Funding

This work was supported by JSPS KAKENHI Grant Number JP23K03141.

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Authors and Affiliations

  1. Department of Information and Computer Engineering, National Institute of Technology, Kisarazu College, 2-11-1 Kiyomidai-Higasi, Kisarazu, Chiba,  292-0041, Japan

    Shuhei Wada

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  1. Shuhei Wada
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Correspondence to Shuhei Wada.

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Wada, S. Extended power difference means. Acta Sci. Math. (Szeged) (2024). https://doi.org/10.1007/s44146-024-00137-7

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