拟Banach空间上含参数的二次-可加混合型函数方程的解和Hyers-Ulam-Rassias稳定性

数学物理学报 ›› 2017, Vol. 37 ›› Issue (5): 846-859.

拟Banach空间上含参数的二次-可加混合型函数方程的解和Hyers-Ulam-Rassias稳定性

王春^1,2, 许天周¹

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

收稿日期:2016-06-14 修回日期:2017-02-27 出版日期:2017-10-26 发布日期:2017-10-26
通讯作者: 王春,E-mail:wangchun12001@163.com E-mail:wangchun12001@163.com
基金资助:
国家自然科学基金（11171022）

Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces

Wang Chun^1,2, Xu Tianzhou¹

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

Received:2016-06-14 Revised:2017-02-27 Online:2017-10-26 Published:2017-10-26
Supported by:
Supported by the NSFC (11171022)

摘要/Abstract

摘要： 该文讨论了带有参数s的二次-可加混合型函数方程
2k[f（x+ky）+f（kx+y）]
=k（1-s+k+ks+2k²）f（x+y）+k（1-s-3k+ks+2k²）f（x-y）
+2kf（kx）+2k（s+k-ks-2k²）f（x）+2（1-k-s）f（ky）+2ksf（y）
的一般解，同时研究了该函数方程在拟Banach空间上的Hyers-Ulam-Rassias稳定性，这里k>1，s≠1-2k.

关键词: Hyers-Ulam-Rassias稳定性, 一般解, 可加映射, 二次映射, 拟Banach空间, p-Banach空间

Abstract: This paper establishes the general solution of the mixed type quadratic-additive functional equation
2k[f(x+ky)+f(kx+y)]
=k(1-s+k+ks+2k²)f(x+y)+k(1-s-3k+ks+2k²)f(x-y)
+2kf(kx)+2k(s+k-ks-2k²)f(x)+2(1-k-s)f(ky)+2ksf(y)
with a parameter s, and investigates the Hyers-Ulam-Rassias stability of this functional equation in quasi-Banach spaces, where k > 1 and s ≠1-2k.

Key words: Hyers-Ulam-Rassias stability, General solution, Additive function, Quadratic function, Quasi-Banach space, p-Banach space

中图分类号:

O177.9

王春, 许天周. 拟Banach空间上含参数的二次-可加混合型函数方程的解和Hyers-Ulam-Rassias稳定性[J]. 数学物理学报, 2017, 37(5): 846-859.

Wang Chun, Xu Tianzhou. Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces[J]. Acta mathematica scientia,Series A, 2017, 37(5): 846-859.

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