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 doi:

DOI: 10.3724/SP.J.1249.2018.01099

Journal of Shenzhen University Science and Engineering (深圳大学学报理工版) 2018/35:1 PP.99-104

## The Ulam stability of functional equation on matrix random normed spaces

• SONG Aimin 1   LI Yuewu 1
• 1.Department of Mathematics, Gansu Normal University for Nationalities, Hezuo 747000, Gansu Province, P. R. China

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.

Key words：fundamental mathematics,random normed spaces,matrix random normed spaces,fixed point method,functional equation deriving from quartic and cubic functions,Ulam stability

ReleaseDate：2018-03-20 15:26:56

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