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Functional inequalities associated with Jordan-von Neumann-type additive functional equations. (English) Zbl 1133.39024

Summary: We prove the generalized Hyers-Ulam stability of the following functional inequalities:
\[ \begin{aligned} \| f(x)+f(y)+f(z)\| &\leq \| 2f((x+y+z)/2)\|, \\ \| f(x)+f(y)+f(z)\| &\leq \| f(x+y+z)\|, \\ \| f(x)+f(y)+2f(z)\|&\leq \| 2f((x+y)/2+z)\| \end{aligned} \]
in the spirit of the Rassias stability approach for approximately homomorphisms.

MSC:

39B62 Functional inequalities, including subadditivity, convexity, etc.
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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References:

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