Stability of a functional equation deriving from quartic and additive functions

TL;DR

This paper investigates the general solutions and stability properties of a complex functional equation involving quartic and additive functions, expanding understanding of its behavior and robustness.

Contribution

It provides the first comprehensive analysis of the general solution and Hyers-Ulam-Rassias stability for this specific functional equation.

Findings

Derived the general solution of the functional equation.

Established the Hyers-Ulam-Rassias stability conditions.

Extended stability results to broader function classes.

Abstract

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation $$f(2x+y)+f(2x-y)=4(f(x+y)+f(x-y))-{3/7}(f(2y)-2f(y))+2f(2x)-8f(x).$$