Stability of a mixed type quadratic, cubic and quartic functional equation

TL;DR

This paper investigates the general solutions and stability properties of a complex functional equation involving quadratic, cubic, and quartic terms, providing insights into its behavior and solutions.

Contribution

It derives the general solution and establishes the Hyers-Ulam-Rassias stability for a specific mixed-type functional equation.

Findings

General solution of the functional equation obtained

Hyers-Ulam-Rassias stability established

Provides a framework for analyzing similar complex equations

Abstract

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation $$3(f(x+2y)+f(x-2y))=12(f(x+y)+f(x-y))+4f(3y)-18f(2y)+36f(y)-18f(x).$$