Functional inequalities for generalized multi-quadratic mappings

Abstract

Abstract In this article, we introduce some special several variables mappings which are quadratic in each variable and show that such mappings can be defined as a single equation that is the generalized multi-quadratic functional equation. We also apply a fixed point theorem to establish the Hyers–Ulam stability for the generalized multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to some known stability results.

Keywords

• Banach space
• (Generalized) Hyers–Ulam stability
• Generalized multi-quadratic mapping
• Fixed point method