Existence of solutions of polynomial-like iterative equation with discontinuous known functions

被引：0

作者：

Yu, Zhiheng ^{[1
]}

Liu, Jinghua ^{[2
]}

机构：

[1] Southwest Jiaotong Univ, Sch Math, Chengdu 611756, Sichuan, Peoples R China

[2] Lingnan Normal Univ, Sch Math & Stat, Zhanjiang 524048, Guangdong, Peoples R China

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2021年 / 23卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Polynomial-like iterative equation; piecewise bi-Lipschitz function; Banach's fixed point principle; INVARIANT CURVES; CONVEX SOLUTIONS; STABILITY;

D O I：

10.1007/s11784-021-00871-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The polynomial-like iterative equation is an extension to the Babbage's equation. It plays an important role in the study of dynamical systems or the iterative theory. Looking for its solutions is an interesting and difficult problem. In this paper, we consider the case that the known function is discontinuous. To overcome the difficulty that the known function is not Lipschitz, we introduce the piecewise bi-Lipschitz functions and construct a completed functional space consisting of such functions. Furthermore, we define an operator to prove the existence of solutions by means of Banach's fixed point principle.

引用

页数：11

共 32 条

[1]

[Anonymous], 1990, ENCY MATH ITS APPL

[2]

[Anonymous], 1997, J. Diff. Eqs. Appl

[3]

Dhombres JG., 1977, PUBL MATH-DEBRECEN, V24, P177

[4]

Dubbey J. M., 1978, MATH WORK CHARLES BA, DOI [10.1017/CBO9780511622397, DOI 10.1017/CBO9780511622397]

[5]

Jarczyk W., 1996, AEQUATIONES MATH, V51, P303, DOI DOI 10.1007/BF01833285

[6]

Kuczma M., 1968, FUNCTIONAL EQUATIONS

[7] Analytic invariant curves for a second order difference equation modelled from macroeconomics under the Brjuno condition [J].

Liu, Jing Hua .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2017, 23 (03) :648-656

[8] Invariant curves for a second-order difference equation modelled from macroeconomics [J].

Liu, Jinghua ;

Yu, Zhiheng ;

Zhang, Weinian .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2015, 21 (09) :757-773

[9] Existence, uniqueness and stability of Cm solutions of iterative functional equations [J].

Mai, JH ;

Liu, XH .

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 2000, 43 (09) :897-913

[10] Characteristic analysis for a polynomial-like iterative equation [J].

Matkowski, J ;

Zhang, WN .

CHINESE SCIENCE BULLETIN, 1998, 43 (03) :192-196

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