Article ID: MTJPAM-D-22-00015

Title: Hom-derivations in Banach Algebras


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-22-00015; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 282-291

Document Type: Research Paper

Author(s): Siriluk Paokanta a , Jung Rye Lee b , Choonkil Park c

aDepartment of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

bDepartment of Data Science, Daejin University, Kyunggi 11159, Korea

cDepartment of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received:4 April 2022, Accepted:25 December 2022, Published:13 February 2023.

Corresponding Author: Jung Rye Lee (Email address: jrlee@daejin.ac.kr)

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Abstract

In this paper, we introduce hom-derivations in complex Banach algebras. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of hom-derivations in complex Banach algebras, associated with the bi-additive s-functional inequality

\| f(x+y, z-w) + f(x-y, z+w) -2f(x,z)+2 f(y, w)\| \le \|s \left(2f\left(\frac{x+y}{2}, z-w\right) + 2f\left(\frac{x-y}{2}, z+w\right) - 2f(x,z )+ 2 f(y, w)\right)\|

where s is a fixed nonzero complex number with |s|<1.

Keywords: Hom-biderivation, Complex Banach algebra, Hyers-Ulam stability, Fixed point method, Bi-additive s-functional inequality

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