﻿ 一类函数方程的周期性 Periodicity of a Class of Functional Equations

Pure Mathematics
Vol.07 No.03(2017), Article ID:20482,4 pages
10.12677/PM.2017.73016

Periodicity of a Class of Functional Equations

Xiaoli Zhou1, Tiejun Zhou1,2

1College of Science, Hunan Agricultural University, Changsha Hunan

2College of Orient Science and Technology, Hunan Agricultural University, Changsha Hunan

Received: Apr. 22nd, 2017; accepted: May 6th, 2017; published: May 10th, 2017

ABSTRACT

The sufficient conditions are obtained that the is a periodic function with period 2T, 3T or 4T for the functional equation. The results generalize the existing conclusions.

Keywords:Functional Equation, Period

1湖南农业大学理学院，湖南 长沙

2湖南农业大学东方科技学院，湖南 长沙

1. 引言

(1)

2. 主要定理

(i) 如果，那么是周期为2T的函数。

(ii) 如果，那么是周期为3T的函数。

(iii) 如果，那么是周期为4T的函数。

(2)

(3)

(i) 如果，则由(3)式可得，即是周期为2T的函数。

(ii) 由(2)式得

(4)

(iii) 由(3)式得

3. 几个实例

4. 结论

Periodicity of a Class of Functional Equations[J]. 理论数学, 2017, 07(03): 137-140. http://dx.doi.org/10.12677/PM.2017.73016

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