# On the General Solution of a Quadratic Functional Equation and its Ulam Stability in Various Abstract Spaces

Volume 7, Issue 6, pp 368--378
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### Authors

Yonghong Shen - School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, P. R. China. Yaoyao Lan - Department of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan 402160, P. R. China.

### Abstract

In this paper, we establish the general solution of a new quadratic functional equation $f ( x -\frac{ y+z}{ 2} ) + f ( x + \frac{y-z}{ 2}) +f(x+z) = 3f(x)+ \frac{1}{ 2}f(y)+ \frac{3}{ 2}f(z)$. Next, the Ulam stability of this equation in a real normed space and a non-Archimedean space is studied, respectively.

### Keywords

• General solution
• Ulam stability
• Quadratic functional equation
• Normed space
• Non-Archimedean space.

•  39A30
•  97I70

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