# On the Ulam stability of a quadratic set-valued functional equation

Volume 7, Issue 5, pp 359--367
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### Authors

Faxing Wang - Tongda College of Nanjing University of Posts and Telecommunications, Nanjing 210046, P. R. China. Yonghong Shen - School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, P. R. China.

### Abstract

In this paper, we prove the Ulam stability of the following set-valued functional equation by employing the direct method and the fixed point method, respectively, $f ( x -\frac{ y + z}{ 2}) \oplus f (x +\frac{ y - z}{ 2})\oplus f(x + z) = 3f(x) \oplus \frac{1}{ 2} f(y) \oplus \frac{3 }{2 }f(z).$

### Share and Cite

##### ISRP Style

Faxing Wang, Yonghong Shen, On the Ulam stability of a quadratic set-valued functional equation, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 5, 359--367

##### AMA Style

Wang Faxing, Shen Yonghong, On the Ulam stability of a quadratic set-valued functional equation. J. Nonlinear Sci. Appl. (2014); 7(5):359--367

##### Chicago/Turabian Style

Wang, Faxing, Shen, Yonghong. "On the Ulam stability of a quadratic set-valued functional equation." Journal of Nonlinear Sciences and Applications, 7, no. 5 (2014): 359--367

### Keywords

• Ulam stability
• Hausdorff distance
• fixed point.

•  39B72
•  54H25
•  54C60

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