A new approach to approximate the solution of two general functional equations in quasi-Banach spaces

Abstract

In this paper, we first establish a stability result for a functional equation in single variable in complete b-metric spaces. This result can be applied to prove the stability of various functional equations in quasi-Banach spaces. The perturbation of Schröder equation in quasi-Banach spaces is also proved. As an application of our main result, the stability in the sense of “G.-L. Forti and P. Gǎvruta” for two general functional equations in quasi-Banach spaces is studied. These equations generalize, among others, those characterizing multi-additive and multi-quadratic functions. The present findings extend and generalize the recent main results presented in Ciepliński (2023) [12] and their corollaries.