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A generalized result on the polynomial-like iterative equation

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Abstract

Most results on the polynomial-like iterative equation are given under the condition that the given function is monotone, while a work by L. Liu and X. Gong gets non-monotone PM solutions with height 1 when the given function is of the same case. Removing the condition on height for the given function, we first give a method to assert the nonexistence of C0 solutions, then present equivalent conditions for the existence of PM solutions with finite height. Finally, as an application of the equivalent conditions, we construct the PM solutions in the case that the given function has one fort.

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Authors and Affiliations

  1. College of Science, Binzhou University, Binzhou, 256603, China

    Pingping Zhang

  2. School of Mathematical Sciences and V.C. & V.R. Key Lab of Sichuan Province, Sichuan Normal University, Chengdu, 610068, China

    Yingying Zeng

Authors
  1. Pingping Zhang
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  2. Yingying Zeng
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Corresponding author

Correspondence to Yingying Zeng.

Additional information

The first author is supported by the Natural Science Foundation of Shandong Province (ZR2017MA019) and the Scientific Research Fund of Binzhou University (BZXYL1802); the second author is supported by the National Science Foundation of China (11501394), the Science Research Fund of Sichuan Provincial Education Department (15ZB0041) and funding of School of Mathematical Sciences and V.C. & V.R. Key Lab of Sichuan Province.

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Zhang, P., Zeng, Y. A generalized result on the polynomial-like iterative equation. Acta Math Sci 41, 177–186 (2021). https://doi.org/10.1007/s10473-021-0110-8

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  • DOI: https://doi.org/10.1007/s10473-021-0110-8

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