[1]宋爱民,李跃武.矩阵随机赋范空间上函数方程的Ulam稳定性[J].深圳大学学报理工版,2018,35(No.1(001-110)):99-104.[doi:10.3724/SP.J.1249.2018.01099]
 SONG Aimin and LI Yuewu.The Ulam stability of functional equation on matrix random normed spaces[J].Journal of Shenzhen University Science and Engineering,2018,35(No.1(001-110)):99-104.[doi:10.3724/SP.J.1249.2018.01099]
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矩阵随机赋范空间上函数方程的Ulam稳定性()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第35卷
期数:
2018年No.1(001-110)
页码:
99-104
栏目:
数学与应用数学
出版日期:
2018-01-12

文章信息/Info

Title:
The Ulam stability of functional equation on matrix random normed spaces
文章编号:
201801015
作者:
宋爱民李跃武
甘肃民族师范学院数学系, 甘肃合作 747000
Author(s):
SONG Aimin and LI Yuewu
Department of Mathematics, Gansu Normal University for Nationalities,Hezuo 747000, Gansu Province, P.R.China
关键词:
基础数学随机赋范空间矩阵随机赋范空间不动点方法混合3次-4次函数方程Ulam稳定性
Keywords:
fundamental mathematics random normed spaces matrix random normed spaces fixed point method functional equation deriving from quartic and cubic functions Ulam stability
分类号:
O 177.1
DOI:
10.3724/SP.J.1249.2018.01099
文献标志码:
A
摘要:
考察矩阵随机赋范空间上函数方程的Ulam稳定性. 结合矩阵赋范空间和随机赋范空间的定义,给出矩阵随机赋范空间的定义,证明其上的若干性质.利用不动点方法,在矩阵随机赋范空间上分别讨论了混合3次-4次函数方程4[f(3x+y)+f(3x-y)]=12[f(2x+y)+f(2x-y)]-12[f(x+y)+f(x-y)]+f(2y)-8f(y)+30f(2x)-192f(x)为奇映射和偶映射时候的Ulam稳定性,证明了在满足一定的条件下混合3次-4次函数方程在矩阵随机赋范空间上满足Ulam稳定性的结论.
Abstract:
We mainly investigates the Ulam stability of functional equations on matrix random normed spaces. Firstly, combining the definition of matrix normed spaces with the random normed spaces, we obtain the definition of matrix random normed spaces, and prove some properties on the spaces. Then, by using the fixed point method, we discuss the Ulam stability of functional equation deriving from quartic and cubic functions 4[f(3x+y)+f(3x-y)]=12[f(2x+y)+f(2x-y)]-12[f(x+y)+f(x-y)]+f(2y)-8f(y)+30f(2x)-192f(x) when they are odd mapping and even mapping on matrix random normed spaces. In the end, we prove that the functional equation deriving from quartic and cubic functions satisfies the Ulam stability on the matrix random normed spaces under certain conditions.

参考文献/References:

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备注/Memo

备注/Memo:
Received:2017-03-28;Accepted:2017-06-28
Foundation:Scientific Research Foundation of the Higher Education Institutions of Gansu Province(2017A-139)
Corresponding author:Associate professor LI Yuewu. E-mail: liyuewu197201@163.com
Citation:SONG Aimin, LI Yuewu. The Ulam stability of functional equation on matrix random normed spaces[J]. Journal of Shenzhen University Science and Engineering, 2018, 35(1): 99-104.(in Chinese)
基金项目:甘肃省高等学校科研资助项目(2017A-139)
作者简介:宋爱民(1984—),男,甘肃民族师范学院讲师. 研究方向:算子代数及其应用, 函数方程的稳定性. E-mail:songai-min@163.com
引文:宋爱民, 李跃武. 矩阵随机赋范空间上函数方程的Ulam稳定性[J]. 深圳大学学报理工版,2018,35(1):99-104.
更新日期/Last Update: 2017-12-22