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Stability of a Jensen type quadratic-additive functional equation under the approximately conditions. (English) Zbl 1347.39028

Summary: We prove the Hyers-Ulam-Rassias stability of the Jensen type quadratic and additive functional equation \(9f (\frac{x+y+z}{3}) + 4 [f(\frac{x-y}{2}) + f(\frac{y-z}{2}) + f (\frac{z-x}{2})] = 3 [f(x)+f(y)+f(z)]\) under the approximately conditions such as even, odd, quadratic, and additive 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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