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The stability of a quadratic functional equation with the fixed point alternative. (English) Zbl 1189.39031
Summary: J. R. Lee, J. S. An and C. Park [ibid. 2008, Article ID 628178, 8 p. (2008; Zbl 1146.39045)] introduced the quadratic functional equation $$f(2x+y)+f(2x - y)=8f(x)+2f(y)$$ and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.
##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges
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