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

Volume 7, Issue 5, pp 359--367 http://dx.doi.org/10.22436/jnsa.007.05.06

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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, \[f ( x -\frac{ y + z}{ 2}) \oplus f (x +\frac{ y - z}{ 2})\oplus f(x + z) = 3f(x) \oplus \frac{1}{ 2} f(y) \oplus \frac{3 }{2 }f(z).\]

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Keywords

• Ulam stability
• Quadratic set-valued functional equation
• Hausdorff distance
• fixed point.

MSC

•  39B72
•  54H25
•  54C60

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