Characterization and stability analysis of advanced multi-quadratic functional equations

Abstract

In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigate n-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes.

An example for the non-stability of multi-additive-quadratic-cubic mappings

“…r is a multiadditive-quadratic-cubic mapping. We remember that the celebrated Ulam query [11] about the stability of group homomorphisms has been studied and established for multivariable mappings such as 2 A. BODAGHI multi-additive, multi-quadratic and multi-cubic mappings for instance in [2], [6], [7], [8], [9], [10] and [12].…”

On the stability of the Pexider system of bi-additive and bi-quadratic equations

“…During the last years, a number of results concerning the stability have been obtained by different ways [5,6,7,8,9,10,11], and been applied to a number of functional equations, functional inequalities and mappings.…”

Characterization and Stability of Multi-Euler-Lagrange Quadratic Functional Equations

“…Park was the first author who studied the stability of multiquadratic in the setting of Banach algebras [16]. After that, some authors introduced various versions of multiquadratic mappings and investigated the Hyers-Ulam stability of such mappings in Banach spaces and non-Archimedean spaces; these results are available for instance in [15,[25][26][27][28][29]. As for an unification of the Definition 1.…”