Commun. Korean Math. Soc. 2022; 37(3): 801-812
Online first article May 13, 2022 Printed July 31, 2022
https://doi.org/10.4134/CKMS.c210300
Copyright © The Korean Mathematical Society.
Abasalt Bodaghi, Hassan Feizabadi
Islamic Azad University; Islamic Azad University
In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers--Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.
Keywords: Derivation, Hyers--Ulam stability, multi-derivation, fixed point method
MSC numbers: 39B52, 39B72, 47H10
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