Stability of the Jensen--type functional equation in ternary Banach algebras: An alternative fixed point approach

TL;DR

This paper establishes the stability of a Jensen-type functional equation in ternary Banach algebras using fixed point methods, demonstrating the generalized Hyers--Ulam--Rassias stability of ternary homomorphisms and multipliers.

Contribution

It introduces an alternative fixed point approach to prove the stability of the Jensen-type functional equation in ternary Banach algebras.

Findings

Proves stability of the functional equation using fixed point methods.

Shows the stability of ternary homomorphisms and multipliers.

Provides a new approach to functional equation stability in algebraic structures.

Abstract

Using fixed point methods, we prove the generalized Hyers--Ulam--Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen--type functional equation $$f(\frac{x+y+z}{3})+f(\frac{x-2y+z}{3})+f(\frac{x+y-2z}{3})= f(x).$$