On the Ulam stability of an n-dimensional quadratic functional equation
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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.
Share and Cite
ISRP Style
Yonghong Shen, Wei Chen, On the Ulam stability of an n-dimensional quadratic functional equation, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 1, 332--341
AMA Style
Shen Yonghong, Chen Wei, On the Ulam stability of an n-dimensional quadratic functional equation. J. Nonlinear Sci. Appl. (2016); 9(1):332--341
Chicago/Turabian Style
Shen, Yonghong, Chen, Wei. "On the Ulam stability of an n-dimensional quadratic functional equation." Journal of Nonlinear Sciences and Applications, 9, no. 1 (2016): 332--341
Keywords
- Ulam stability
- n-dimensional quadratic functional equation
- normed space
- non-Archimedean space.
MSC
References
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