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Research Article | Open Access

Stability of hyper homomorphisms and hyper derivations in complex Banach algebras

Yamin Sayyari1( ), Mehdi Dehghanian1, Choonkil Park2( ), Jung Rye Lee3( )
Department of Mathematics, Sirjan University of Technology, Sirjan, Iran
Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea
Department of Data Science, Daejin University, Kyunggi 11159, Korea
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Abstract

In this paper, we introduce the concept of hyper homomorphisms and hyper derivations in Banach algebras and we establish the stability of hyper homomorphisms and hyper derivations in Banach algebras for the following 3-additive functional equation:

g ( x 1 + x 2 , y 1 + y 2 , z 1 + z 2 ) = ∑ i , j , k = 1 2 g ( x i , y j , z k ) .

Keywords

Hyers-Ulam stability3-additive functional equationhyper derivationhyper homomrphism3-linear mapping
CLC number: 17B40, 39B52, 39B62, 39B72, 47B47

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10700-10710
DOI: 10.3934/math.2022597

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Cite this article:
Sayyari Y, Dehghanian M, Park C, et al. Stability of hyper homomorphisms and hyper derivations in complex Banach algebras. AIMS Mathematics, 2022, 7(6): 10700-10710. https://doi.org/10.3934/math.2022597

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Received: 15 January 2022
Revised: 23 March 2022
Accepted: 25 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)