On the General Solution of a Quadratic Functional Equation and its Ulam Stability in Various Abstract Spaces
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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.
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ISRP Style
Yonghong Shen, Yaoyao Lan, On the General Solution of a Quadratic Functional Equation and its Ulam Stability in Various Abstract Spaces, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 6, 368--378
AMA Style
Shen Yonghong, Lan Yaoyao, On the General Solution of a Quadratic Functional Equation and its Ulam Stability in Various Abstract Spaces. J. Nonlinear Sci. Appl. (2014); 7(6):368--378
Chicago/Turabian Style
Shen, Yonghong, Lan, Yaoyao. "On the General Solution of a Quadratic Functional Equation and its Ulam Stability in Various Abstract Spaces." Journal of Nonlinear Sciences and Applications, 7, no. 6 (2014): 368--378
Keywords
- General solution
- Ulam stability
- Quadratic functional equation
- Normed space
- Non-Archimedean space.
MSC
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