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.


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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