HYPERSTABILITY OF A CAUCHY FUNCTIONAL EQUATION

M.  ALMAHALEBI; A.  CHARIFI; S.  KABBAJ

HYPERSTABILITY OF A CAUCHY FUNCTIONAL EQUATION

Authors

M. ALMAHALEBI Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP: 133, 14000, KENITRA, MOROCCO
A. CHARIFI Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP: 133, 14000, KENITRA, MOROCCO
S. KABBAJ Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP: 133, 14000, KENITRA, MOROCCO

Keywords:

Hyperstability, Cauchy equation, Fixed point theorem

Abstract

The aim of this paper is to offer hyperstability results for the Cauchy functional equation $$f\left(\sum_{i=1}^{n}x_{i}\right)=\sum_{i=1}^{n}f(x_{i})$$ in Banach spaces. Namely, we show that a function satisfying the equation approximately must be actually a solution to it.