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

Safoura Rezaei Aderyani, Reza Saadati (), Donal O’Regan and Chenkuan Li
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Safoura Rezaei Aderyani: School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
Reza Saadati: School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
Donal O’Regan: School of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, Ireland
Chenkuan Li: Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada

Mathematics, 2023, vol. 11, issue 16, 1-35

Abstract: 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.

Keywords: multi stability; approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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