In this article, by using a new form of multi-quadratic mapping, we define multi- m -Jensen-quadratic mappings and then unify the system of functional equations defining a multi- m -Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of multi-quadratic and multi- m -Jensen-quadratic functional equations. As a consequence, we show that every multi- m -Jensen-quadratic functional equation (under some conditions) can be hyperstable.

中文翻译：

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多个m-Jensen二次映射的逼近和不动点方法

在本文中，通过使用一种新的多二次映射形式，我们定义了多m次詹森二次映射，然后将定义多次m次詹森二次映射的功能方程组统一为一个方程。使用不动点定理，我们研究了多二次方程和多m-詹森二次方程的广义Hyers-Ulam稳定性。结果，我们证明了每个m-Jensen二次函数方程（在某些条件下）都可以是超稳定的。