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On the Hyers–Ulam stability and hyperstability of a generalized quadratic functional equation in $n$ $n$ -Banach spaces

Nordine Bounader

Laboratory Analysis, Geometry and Applications, Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, Kenitra, Morocco

E-mail Address: n.bounader@live.fr

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https://doi.org/10.1142/S1793557122500139Cited by:1 (Source: Crossref)

Abstract

In this paper, we establish some Hyers–Ulam stability and hyperstability results of the following functional equation

\sum_{ψ \in K_{n - 1}} f (ψ (x_{1}, x_{2}, \dots, x_{n})) = 2^{n - 1} \sum_{i = 1}^{n} f (x_{i})

in the class of functions from an abelian group

X

$X$ into a

n

$n$ -Banach space.

Communicated by A. Akhmedov

Keywords:

AMSC: 39B82, 39B52, 47H14, 47H10

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