On the Ulam stability of an n-dimensional quadratic functional equation

Volume 9, Issue 1, pp 332--341 http://dx.doi.org/10.22436/jnsa.009.01.31

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Authors

Yonghong Shen - School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, P. R. China. - School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China. Wei Chen - School of Information, Capital University of Economics and Business, Beijing, 100070, P. R. China.

Abstract

In the present paper, we construct a new n-dimensional quadratic functional equation with constant coefficients \[\sum^n_{i,j=1}f(x_i+x_j)=2\sum^n_{1\leq i< j\leq n}f(x_i-x_j)+4f\left(\sum^n_{i=1}x_i\right)\] And then, we study the Ulam stability of the preceding equation in a real normed space and a non- Archimedean space, respectively.

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Keywords

• Ulam stability
• n-dimensional quadratic functional equation
• normed space
• non-Archimedean space.

MSC

•  39A30
•  97I70

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