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Square iterative roots of generalized weighted quasi-arithmetic mean-type mappings

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Abstract

We determine all pairs \((A_{f,g},A_{g,h})\) of generalized weighted quasi-arithmetic means being square iterative roots of \((A_{F,G},A_{G,H})\), that is, the equation \begin{equation*} ( A_{f,g},A_{g,h}) \circ ( A_{f,g},A_{g,h}) =(A_{F,G},A_{G,H}), \end{equation*} is solved under three times differentiability of the functions \(f, g, h, F, G, H\). As an application, some special cases are presented.

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Acknowledgement

The authors are very grateful to the reviewer for carefully checking and helpful suggestions.

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Authors and Affiliations

  1. College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang, 314001, P. R. China

    L. Li

  2. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, PL, 65-516, Zielona Góra, Poland

    J. Matkowski

  3. School of Science, Southwest University of Science and Technology, Mianyang, Mianyang, Sichuan, 621010, P. R. China

    Q. Zhang

Authors
  1. L. Li
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  2. J. Matkowski
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  3. Q. Zhang
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Corresponding author

Correspondence to L. Li.

Additional information

This work was partially supported by Zhejiang Provincial Natural Science Foundation of China under Grant #LY18A010017 and the National Science Foundation of China Grant #11671061.

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Li, L., Matkowski, J. & Zhang, Q. Square iterative roots of generalized weighted quasi-arithmetic mean-type mappings. Acta Math. Hungar. 163, 149–167 (2021). https://doi.org/10.1007/s10474-020-01126-2

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  • DOI: https://doi.org/10.1007/s10474-020-01126-2

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