## Hyers-Ulam-Rassias stability of Jensen’s equation and its application.(English)Zbl 0909.39014

The author examines the Hyers-Ulam-Rassias stability [see D. H. Hyers, G. Isac and Th. M. Rassias, Stability of functional equations in several variables, Birkhäuser, Boston (1998)] of the Jensen functional equation and proves that a mapping $$f$$ from a real normed space $$X$$ into a real Banach space $$Y$$ satisfying $$f(0)=0$$ is additive if and only if $$\| 2f((x+y)/2) -f(x)- f(y)\|\to 0$$ as $$\| x\| +\| y\|\to \infty$$.

### MSC:

 39B72 Systems of functional equations and inequalities 39B52 Functional equations for functions with more general domains and/or ranges
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