On the Stability of an Additive and Quadratic Functional Equation
作者： Choonkil Park
DOI: 10.1007/978-1-4614-3498-6_34
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摘要: In Park et al. (J. Chungcheong Math. Soc. 21:455–466, 2008) considered the following Jensen additive and quadratic type functional equation $$2 f \biggl(\frac{x+y}{2} \biggr) + \biggl( \frac{x-y}{2} \biggr ) \biggl(\frac{y-x}{2} = f(x) f(y) . $$ In this paper, we investigate $$ 2 f(x+y) f(x-y) f(y-x) 3f(x) f(-x) 3f(y) f(-y) $$ (34.1) Furthermore, prove generalized Hyers–Ulam stability of (34.1) in Banach spaces.
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