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

Abstract

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),f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where ff maps from a (β,p)\left(\beta ,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 ss-functional inequality is discussed via our results.

Keywords

• additive functional equations
• composite functional equations
• composite s-functional inequalities
• quasi-β-normed spaces
• 39b32
• 30d05
• 47h10
• 46h25