Banach 空间三次方程的稳定性问题

数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 266-273.

Banach 空间三次方程的稳定性问题

成立花¹|连铁艳²

1.西安工程大学理学院西安 710048|2.陕西科技大学理学院西安 710021

收稿日期:2012-10-08 修回日期:2013-04-06 出版日期:2014-04-25 发布日期:2014-04-25
基金资助:
陕西省教育厅自然科学专项基金(12jk0879)资助.

Stability of Cubic Functional Equations in Banach Spaces

CHENG Li-Hua¹, LIAN Tie-Yan²

1.College Science, Xian Polytechnic University, Xi'an 710048|2.College Science, Shanxi University of Science &|Technology, Xi'an 710021

Received:2012-10-08 Revised:2013-04-06 Online:2014-04-25 Published:2014-04-25
Supported by:
陕西省教育厅自然科学专项基金(12jk0879)资助.

摘要/Abstract

摘要：

给出了三次 Hyers-Ulam-Rassias 型泛函方程的一种新表示方法af(x+ay)-f(ax+y)=a(a²-1)/2[f(x+y)+f(x-y)]+(a⁴-1)f(y)-2a(a²-1)f(x), 其中a为整数且a≠0, ±1. 关于9个三次泛函方程给出等价性证明. 对Banach 空间三次方程的稳定性问题给予讨论.

关键词: 稳定性, 三次泛函方程, Jordan 同态

Abstract:

In this note, we will find out the general solution and investigate the Hyers-Ulam-Rassias stability of a cubic functional equation af(x+ay)-f(ax+y)=a(a²-1)/2[f(x+y)+f(x-y)]+(a⁴-1)f(y)-2a(a²-1)f(x), in Banach spaces for a fixed integer a with a≠0, ±1. Forthermore, we give the equivalent proof of eight functional equations. At last, the stability of cubic functional equation in Banach spaces is dissucied.

Key words: Stability, Cubic equation, Jordan homorphism

中图分类号:

39B52

成立花, 连铁艳. Banach 空间三次方程的稳定性问题[J]. 数学物理学报, 2014, 34(2): 266-273.

CHENG Li-Hua, LIAN Tie-Yan. Stability of Cubic Functional Equations in Banach Spaces[J]. Acta mathematica scientia,Series A, 2014, 34(2): 266-273.

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