On the Stability of Additive, Quadratic, Cubic and Quartic Set-valued Functional Equations

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• 作者：Hamid Khodaei
• 关键词：54C60 ; 47H10 ; 47H04 ; 39B82 ; 39B52 ; Set ; valued map ; contractively subhomogeneous map ; expansively superhomogeneous map ; stability ; fixed point
• 刊名：Results in Mathematics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：68
• 期：1-2
• 页码：1-10
• 全文大小：483 KB
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• 作者单位：Hamid Khodaei (1)
  
  1. Department of Mathematics, Malayer University, P.O. Box 65719-95863, Malayer, Iran
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9012

文摘

For m = 1, 2, 3, 4, we study the following set-valued functional equation $$\begin{array}{ll}f(ax + y) \oplus f(ax - y) = a^{m-2}[f(x + y) \oplus f(x - y)] \oplus 2(a^{2} - 1) [a^{m-2}f(x) \\ \quad \oplus \frac{(m - 2)(1 - (m - 2)^{2})}{6}f(y)]\end{array}$$