二元混合五次函数方程的稳定性

J4 ›› 2013, Vol. 48 ›› Issue (10): 9-13.

二元混合五次函数方程的稳定性

纪培胜,刘荣荣

青岛大学数学科学学院, 山东青岛 266071

收稿日期:2012-12-19 发布日期:2013-10-14
作者简介:纪培胜(1967- ), 男,博士, 教授, 研究方向为算子代数. Email:jipeish@yahoo.com
基金资助:
国家自然科学基金资助项目(10971117)

The Hyers-Ulam-Rassias stability of a mixed quintic functional equation of two variables

JI Pei-sheng, LIU Rong-rong

School of Mathematics, Qingdao University, Qingdao 266071, Shandong, China

Received:2012-12-19 Published:2013-10-14

摘要/Abstract

摘要：

设X和Y分别是实向量空间和实Banach空间,映射f:X2→Y称为二元混合五次函数是指任给x1, x2, y1, y2∈X都满足方程f(x1+x2, 2y1+y2)+f(x1+x2, 2y1-y2)+f(x1-x2, 2y1+y2)+f(x1-x2, 2y1-y2)=4f(x1, y1+y2)+4f(x2,y1+y2)+4f(x1,y1-y2)+4f(x2,y1-y2)+24f(x1,y1)+24f(x2,y1)。给出了二元混合五次方程的一般解,并证明了它的Hyers-Ulam-Rassias稳定性。

关键词: Hyers-Ulam-Rassias稳定性;二元混合五次函数方程; Banach空间

Abstract:

Let X be a vector space and Y be a Banach space over the real field, R. A mapping f:X2→Y from X2 into Y is called a mixed quintic functional equation of two variables if it satisfies that f(x1+x2, 2y1+y2)+f(x1+x2,2y1-y2)+f(x1-x2, 2y1+y2)+f(x1-x2, 2y1-y2)=4f(x1,y1+y2)+4f(x2, y1+y2)+4f(x1,y1-y2)+4f(x2, y1-y2)+24f(x1, y1)+24f(x2, y1) for all x1, x2, y1, y2∈X. The general solution of the mixed quintic functional equation of two variables is obtained and the Hyers-Ulam-Rassias stability for it is proved.

Key words: Hyers-Ulam-Rassias stability; the mixed quintic functional equation of two variables; Banach space

中图分类号:

O177.5

纪培胜,刘荣荣. 二元混合五次函数方程的稳定性[J]. J4, 2013, 48(10): 9-13.

JI Pei-sheng, LIU Rong-rong. The Hyers-Ulam-Rassias stability of a mixed quintic functional equation of two variables[J]. J4, 2013, 48(10): 9-13.

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