Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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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.

Multi-derivations and some approximations

Abasalt Bodaghi, Hassan Feizabadi

Islamic Azad University; Islamic Azad University

Abstract

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