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On new stability results for composite functional equations in quasi-β-normed spaces

Thanyacharoen Anurak, Sintunavarat Wutiphol

Demonstratio Mathematica

2021

Vol. 54, nr 1

68--84

In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x) – f(y)) = f(x + y) + f(x – y) – f(x) – f(y), where f maps from a(β, p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s-functional inequality is discussed via our results.

The new investigation of the stability ofmixed type additive-quartic functionalequations in non-Archimedean spaces

Thanyacharoen Anurak, Sintunavarat Wutiphol

Demonstratio Mathematica

2020

Vol. 53, nr 1

174--192

In this article, we prove the generalized Hyers-Ulam stability for the following additive-quarticfunctional equation: f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) + 24f(y) = 13[ f(x + y) + f(x - y)] + 12f(2y), where f maps from an additive group to a complete non-Archimedean normed space.