Continuous solutions of 3rd-order iterative equation of linear dependence

Advances in Difference Equations

Pingping Zhang¹  Xiaobing Gong² 

[1] Department of Mathematics, Binzhou University, Binzhou, China;Department of Mathematics, Neijiang Normal University, Neijiang, China

关键词: functional equation;    iteration;    characteristic root;    continuous solution;   

DOI  :  10.1186/1687-1847-2014-318

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study continuous solutions of the 3rd-order iterative equation of the linear dependence for hyperbolic cases and generalize the results to the n th-order polynomial-like iterative equation, in some cases recursively. This paper partly answers the question raised in Remark 7 in (Yang and Zhang in Aequ. Math. 67:80-105, 2004) and the open problem raised by Matkowski in (Aequ. Math. 37:119, 1989) in the 26th international symposium on functional equations. MSC:39B12, 37E05.

【 授权许可】

CC BY