Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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MULTI-DERIVATIONS AND SOME APPROXIMATIONS

  • Bodaghi, Abasalt (Department of Mathematics Garmsar Branch Islamic Azad University) ;
  • Feizabadi, Hassan (Department of Mathematics Arak Branch Islamic Azad University)
  • Received : 2021.09.06
  • Accepted : 2022.01.14
  • Published : 2022.07.31
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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

Acknowledgement

The authors sincerely thank the anonymous reviewers for their careful reading, constructive comments to improve the quality of the first draft of paper.

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