A GENERALIZED RESULT ON THE POLYNOMIAL-LIKE ITERATIVE EQUATION

doi:10.1007/s10473-021-0110-8

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 177-186.doi: 10.1007/s10473-021-0110-8

A GENERALIZED RESULT ON THE POLYNOMIAL-LIKE ITERATIVE EQUATION

张萍萍¹, 曾莹莹²

1. College of Science, Binzhou University, Binzhou 256603, China;
2. School of Mathematical Sciences and V. C. & V. R. Key Lab of Sichuan Province, Sichuan Normal University, Chengdu 610068, China

收稿日期:2019-10-29 修回日期:2020-09-11 出版日期:2021-02-25 发布日期:2021-04-06
通讯作者: Yingying ZENG E-mail:mathyyz@163.com
作者简介:Pingping ZHANG,E-mail:ppz.2005@163.com
基金资助:
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.

A GENERALIZED RESULT ON THE POLYNOMIAL-LIKE ITERATIVE EQUATION

Pingping ZHANG¹, Yingying ZENG²

1. College of Science, Binzhou University, Binzhou 256603, China;
2. School of Mathematical Sciences and V. C. & V. R. Key Lab of Sichuan Province, Sichuan Normal University, Chengdu 610068, China

Received:2019-10-29 Revised:2020-09-11 Online:2021-02-25 Published:2021-04-06
Contact: Yingying ZENG E-mail:mathyyz@163.com
About author:Pingping ZHANG,E-mail:ppz.2005@163.com
Supported by:
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.

摘要/Abstract

摘要： 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 $C^0$ 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.

关键词: height, characteristic interval, fort, PM function

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 $C^0$ 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.

Key words: height, characteristic interval, fort, PM function

中图分类号:

39B12

张萍萍, 曾莹莹. A GENERALIZED RESULT ON THE POLYNOMIAL-LIKE ITERATIVE EQUATION[J]. 数学物理学报(英文版), 2021, 41(1): 177-186.

Pingping ZHANG, Yingying ZENG. A GENERALIZED RESULT ON THE POLYNOMIAL-LIKE ITERATIVE EQUATION[J]. Acta mathematica scientia,Series B, 2021, 41(1): 177-186.

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A GENERALIZED RESULT ON THE POLYNOMIAL-LIKE ITERATIVE EQUATION

A GENERALIZED RESULT ON THE POLYNOMIAL-LIKE ITERATIVE EQUATION

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