Stability of the multi-Jensen equation
Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 133-142
Printed March 1, 2008
Wolfgang Prager and Jens Schwaiger
Karl-Franzens Universit\"at Graz
Abstract : Given an $m\in\mathbb N$ and two vector spaces $V$ and $W$, a function $f:V^m\rightarrow W$ is called multi-Jensen if it satisfies Jensen's equation in each variable separately. In this paper we unify these $m$ Jensen equations to obtain a single functional equation for $f$ and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.
Keywords : stability, multi-Jensen functions
MSC numbers : 39B52
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