A Quick Look at the Stability of the New Generalized Linear Functional Equation

Jedsada Senasukh, Satit Saejung

Abstract

In this paper, we show that the stability of the generalized linear functional equation introduced by Aiemsomboon and Sintunavarat [L. Aiemsomboon, W. Sintunavarat, Stability of the new generalized linear functional equation in normed spaces via the fixed point method in generalized metric spaces, Thai J. Math. 16 (2018) 113--124] follows easily from the well-known results of G\u{a}vru\c{t}a [P. G\u avru\c ta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mapping, J. Math. Anal. Appl. 184 (1994) 431--436] and Jung [S.M. Jung, On the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 204 (1996) 221--226, S.M. Jung, Stability of the quadratic equation of Pexider type, Abh. Math. Sem. Unniv. Hamburg. 70 (2000) 175--190]. Moreover, we show that the new upper bound of our estimate is not only better than the ones proposed by Aiemsomboon and Sintunavarat, but also sharp at least some particular functions.