矩阵赋准范空间中五次泛函方程的稳定性（英文）  

Stability of a quintic functional equation in matrix paranormed spaces

作　　者：王志华[1] WANG Zhihua(School of Science, Hubei University of Technology, Wuhan 430068, Hubei, China)

机构地区：[1]湖北工业大学理学院

出　　处：《上海师范大学学报（自然科学版）》2019年第3期231-241,共11页Journal of Shanghai Normal University(Natural Sciences)

基　　金：The National Natural Science Foundation of China(11401190);Key Project of Educational Department of Hubei Province of China(D20161401);Humanities and Social Sciences of Ministry of Education Planning Fund(17YJA790098)

摘　　要：在矩阵赋准范空间中证明了五次泛函方程f(3x+2y)-5f(2x+2y)+f(2x-2y) + 10f(3x+ 2y)-5f(x-2y) = 10f(y) + f(3x)-3f(2x)-27f(x)的 Hyers-Ulam 稳定性。进而,在矩阵 Banach 空间中研究了该方程的Hyers-Ulam稳定性,且用所获得的结果在L∞-范数Banach空间中证明了该方程Hyers-Ulam稳定性。The main goal of this paper is to prove the Hyers-Ulam stability of the quintic functional equation f(3x + y)- 5f(2x + y)+ f(2x- y)+ 10f(x + y)- 5f(x - y)= 10f(y)+ f(3x)-3f(2x)-27f(x) in matrix paranormed spaces. In addition, we establish results concerning the Hyers-Ulam stability of the above functional equation in matrix Banach spaces, and then apply these results to prove the Hyers-Ulam stability of this functional equation in L1-normed Banach spaces.

关 键 词：HYERS-ULAM稳定性 矩阵赋准范空间 矩阵Banach空间 五次泛函方程 

分 类 号：O29[理学—应用数学]