On approximate cubic homomorphisms

TL;DR

This paper studies the stability of certain functional equations related to cubic homomorphisms on Banach algebras, establishing conditions under which approximate solutions are close to exact solutions.

Contribution

It proves the superstability of a system of functional equations involving cubic homomorphisms on Banach algebras using generalized Hyers--Ulam--Rassias stability methods.

Findings

The system exhibits superstability under suitable control functions.

Approximate solutions are close to true solutions in the Banach algebra setting.

The results extend stability theory to cubic homomorphism equations.

Abstract

In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of the system of functional equations $$f(xy)=f(x)f(y), \qquad\qquad. f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x), $$ on Banach algebras. Indeed we establish the superstability of above system by suitable control functions.