Stability of hyper homomorphisms and hyper derivations in complex Banach algebras

Yamin Sayyari; Mehdi Dehghanian; Choonkil Park; Jung Rye Lee; Yamin Sayyari; Mehdi Dehghanian; Choonkil Park; Jung Rye Lee

doi:10.3934/math.2022597

AIMS Mathematics

2022, Volume 7, Issue 6: 10700-10710. doi: 10.3934/math.2022597

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Research article

Stability of hyper homomorphisms and hyper derivations in complex Banach algebras

1.
Department of Mathematics, Sirjan University of Technology, Sirjan, Iran
2.
Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea
3.
Department of Data Science, Daejin University, Kyunggi 11159, Korea

Received: 15 January 2022 Revised: 23 March 2022 Accepted: 25 March 2022 Published: 30 March 2022
MSC : 17B40, 39B52, 39B62, 39B72, 47B47

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:

$ \begin{align*} g(x_1+x_2, y_1+y_2, z_1+z_2) = \sum\limits_{i, j, k = 1}^2 g(x_i, y_j, z_k). \end{align*} $
- Hyers-Ulam stability,
- 3-additive functional equation,
- hyper derivation,
- hyper homomrphism,
- 3-linear mapping
Citation: Yamin Sayyari, Mehdi Dehghanian, Choonkil Park, Jung Rye Lee. Stability of hyper homomorphisms and hyper derivations in complex Banach algebras[J]. AIMS Mathematics, 2022, 7(6): 10700-10710. doi: 10.3934/math.2022597

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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:

$ \begin{align*} g(x_1+x_2, y_1+y_2, z_1+z_2) = \sum\limits_{i, j, k = 1}^2 g(x_i, y_j, z_k). \end{align*} $

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