2-Banach空间上三次-四次混合型函数方程的Hyers-Ulam-Rassias稳定性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 352-368.

2-Banach空间上三次-四次混合型函数方程的Hyers-Ulam-Rassias稳定性

王春^1,*(),许天周²

¹ 长治学院数学系山西长治 046011
² 北京理工大学数学与统计学院北京 100081

收稿日期:2018-10-15 出版日期:2020-04-26 发布日期:2020-05-21
通讯作者: 王春 E-mail:wangchun12001@163.com
基金资助:
山西省自然科学基金(201801D121024);山西省高等学校科技创新项目(2019L0903)

Hyers-Ulam-Rassias Stability of a Mixed Type Cubic-Quartic Functional Equation in 2-Banach Spaces

Chun Wang^1,*(),Tianzhou Xu²

¹ Department of Mathematics, Changzhi University, Shanxi Changzhi 046011
² School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081

Received:2018-10-15 Online:2020-04-26 Published:2020-05-21
Contact: Chun Wang E-mail:wangchun12001@163.com
Supported by:
the NSF of Shanxi Province(201801D121024);the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (STIP)(2019L0903)

摘要/Abstract

摘要：

该文研究了2-Banach空间上三次-四次混合型函数方程

$\begin{eqnarray*} &&f(kx+y)+f(kx-y)\\ & = & \frac{k^2+k}{2}[f(x+y)+f(x-y)]+\frac{k^2 -k}{2}[f(-x-y)+f(y-x)]\\ && +(k^4+k^3-k^2 -k)f(x)+(k^4-k^3-k^2+k)f(-x)-(k^2 -1)f(y)-(k^2 -1)f(-y) \end{eqnarray*}$

的一般解和Hyers-Ulam-Rassias稳定性，这里k>1.该文的结果提升和推广了已有的相关结果.

关键词: Hyers-Ulam-Rassias稳定性, 一般解, 三次映射, 四次映射, 2-Banach空间

Abstract:

In this paper, we investigate the general solution and the Hyers-Ulam-Rassias stability of the mixed type cubic-quartic functional equation

in 2-Banach spaces, where k >1. The results improve and extend some recent results.

Key words: Hyers-Ulam-Rassias stability, General solution, Cubic function, Quartic function, 2-Banach space

中图分类号:

O177.9

王春,许天周. 2-Banach空间上三次-四次混合型函数方程的Hyers-Ulam-Rassias稳定性[J]. 数学物理学报, 2020, 40(2): 352-368.

Chun Wang,Tianzhou Xu. Hyers-Ulam-Rassias Stability of a Mixed Type Cubic-Quartic Functional Equation in 2-Banach Spaces[J]. Acta mathematica scientia,Series A, 2020, 40(2): 352-368.

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