On the stability of ∗-derivations on Banach ∗-algebras

Park, Choonkil; Bodaghi, Abasalt

doi:10.1186/1687-1847-2012-138

Cited by 21 publications

(12 citation statements)

References 12 publications

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“…Recently, in [21], Park and Bodaghi proved the stability and the superstability of * -derivations associated with the Cauchy functional equation and the Jensen functional equation by the mentioned theorem (for more applications, see [22][23][24][25][26][27][28]).…”

Section: Superstability: a Fixed Point Approachmentioning

confidence: 99%

Approximately Ternary Homomorphisms onC*-Ternary Algebras

Shim

Kwon

Hyen

et al. 2013

Abstract and Applied Analysis

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Gordji et al. established the Hyers-Ulam stability and the superstability ofC*-ternary homomorphisms andC*-ternary derivations onC*-ternary algebras, associated with the following functional equation:fx2-x1/3+fx1-3x3/3+f3x1+3x3-x2/3=fx1, by the direct method. Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the conditions and prove the corrected theorems. Furthermore, we prove the Hyers-Ulam stability and the superstability ofC*-ternary homomorphisms andC*-ternary derivations onC*-ternary algebras by using a fixed point approach.

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Section: Superstability: a Fixed Point Approachmentioning

confidence: 99%

Approximately Ternary Homomorphisms onC*-Ternary Algebras

Shim

Kwon

Hyen

et al. 2013

Abstract and Applied Analysis

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“…Jang and Park ([10]) investigated the stability of * -derivations and of quadratic * -derivations with Cauchy functional equation and the Jensen functional equation on Banach * -algebra. The stability of * -derivations on Banach * -algebra by using fixed point alternative was proved by Park and Bodaghi and also Yang et al; see ( [14]) and ( [22]), respectively. Also, the stability of cubic Lie derivations was introduced by Fošner and Fošner; see ( [5]).…”

Section: Introductionmentioning

confidence: 99%

A fixed point approach to the stability of sextic Lie *-derivations

Kang

Koh

2017

Filomat

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“…Especially, Jang and Park [9] introduced the concepts of * -derivations and investigated the stability problems of quadratic * -derivations on Banach C * -algebra. Also, Park and Bodaghi and Yang et al studied the stability properties of * -derivations by using an alternative fixed point method; see [12] and [19]. Also, Fošner and Fošner introduced the basic concepts of cubic Lie derivations and investigated the stability problem of cubic Lie derivations; see [6].…”

Section: Introductionmentioning

confidence: 99%