Cauchy-Drygas型函数方程的Ulam稳定性  

The Ulam Stability Of Cauchy-Drygas Functional Equation

作　　者：宋爱民[1] SONG Aimin(College of mathematics, Gansu normal University for nationalities, Gannan 747000, Gans)

机构地区：[1]甘肃民族师范学院数学系,甘南甘肃747000

出　　处：《四川师范大学学报（自然科学版）》2016年第6期851-856,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：甘肃省高等学校科研项目(2015B-120)

摘　　要：给出Cauchy-Drygas型函数方程f(x_1+x_2,y_1+y_2)+f(x_1+x_2,y_1-y_2)=2f(x_1,y_1)+2f(x_2,y_1)+f(x_1,y_2)+f(x_2,y_2)+f(x_1,-y_2)+f(x2,-y2)的定义,并得到其一般解,同时,进一步讨论Cauchy-Drygas型函数方程与混合二次-三次函数方程的关系,并在Banach空间及模糊赋范空间上讨论它的Ulam稳定性.In this paper,we define the Cauchy- Drygas functional equation f（x1＋x2,y1＋y2）＋f（x1＋x2,y1-y2）=2f（x1,y1）＋2f（x2,y1）＋f（x1,y2）＋f（x2,y2）＋f（x1,-y2）＋f（x2,-y2）,and obtain its general solution.Moreover,we establish the relationship between Cauchy-Drygas functional equation and quadratic-cubic functional equation,and prove the Ulam stability of Cauchy-Drygas functional equation in Banach space and fuzzy normed space.

关 键 词：Cauchy-Drygas型函数方程 BANACH空间 模糊赋范空间 Ulam稳定性 

分 类 号：O177.1[理学—数学]