- - - Department of Mathematics Garmsar Branchو Islamic Azad Universityو Garmsar, Iran
م - - Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran

In this article, we introduce the multi-$m$-Jensen mappings and characterize them as a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability for such mappings. As a consequence, we show that every multi-$m$-Jensen mappings (under some conditions) is hyperstable.

Banach space, multi-m-Jensen mapping, Hyers-Ulam stability