Stability of ternary Jordan homomorphisms and derivations associated to the generalized Jensen equation

TL;DR

This paper investigates the stability of ternary Jordan homomorphisms and derivations in the context of the generalized Jensen equation, providing conditions under which approximate solutions are close to true algebraic structures.

Contribution

It establishes the generalized Hyers-Ulam stability for Jordan homomorphisms and derivations in ternary algebras related to the generalized Jensen equation.

Findings

Stability results for Jordan homomorphisms

Stability results for Jordan derivations

Conditions for approximate solutions to be exact

Abstract

In this paper, we establish the generalized Hyers-Ulam stability of Jordan homomorphisms and Jordan derivations between ternary algebras via the generalized Jensen equation $rf(\frac{sx+ty}{r})=sf(x)+tf(y)$.