On a New Approach for Stability and Controllability Analysis of Functional Equations

We consider a new approach to approximate stability analysis for a tri-additive functional inequality and to obtain the optimal approximation for permuting tri-derivations and tri-homomorphisms in unital matrix algebras via the vector-valued alternative fixed-point theorem, which is a popular technique of proving the stability of functional equations. We also present a small list of aggregation functions on the classical, well-known special functions to investigate the best approximation error estimates using a different concept of perturbation stability.

Automated summary

In this paper, a new method for approximating stability analysis of a tri-additive functional inequality is considered, and the optimal approximation for permuting tri-derivations and tri-homomorphisms in unital matrix algebras is obtained using the vector-valued alternative fixed-point theorem. Furthermore, a small list of aggregation functions on the classical, well-known special functions is presented to investigate the best approximation error estimates using a different concept of perturbation stability.