Additive s-functional inequalities and derivations on Banach algebras

Taekseung Kim, Younghun Jo, Junha Park, Jaemin Kim, Choonkil Park, Jung Rye Lee

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this paper, we introduce the following new additive s-functional inequalities ||f(x - y) + f(y) + f(-x)II ≤ ||s (f(x + y) - f-x) - f(y)) || (0.1) ||f(x + y) - f-x) - f(y)|| ≤ ||s (f(x - y) + f(y) + f(-x)) ||, (0.2) where s is a _xed complex number with |s| < 1, and prove the Hyers-Ulam stability of linear derivations on Banach algebras associated to the additive s-functional inequalities (0.1) and (0.2).

Original languageEnglish
Pages (from-to)917-924
Number of pages8
JournalJournal of Computational Analysis and Applications
Volume27
Issue number5
StatePublished - 2019 Oct 30

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Functional Inequalities
Banach algebra
Algebra
Hyers-Ulam Stability
Complex number

Keywords

  • Additive s-functional inequality
  • Derivation on Banach algebra
  • Direct method
  • Hyers-Ulam stability

Cite this

Kim, Taekseung ; Jo, Younghun ; Park, Junha ; Kim, Jaemin ; Park, Choonkil ; Lee, Jung Rye. / Additive s-functional inequalities and derivations on Banach algebras. In: Journal of Computational Analysis and Applications. 2019 ; Vol. 27, No. 5. pp. 917-924.
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Additive s-functional inequalities and derivations on Banach algebras. / Kim, Taekseung; Jo, Younghun; Park, Junha; Kim, Jaemin; Park, Choonkil; Lee, Jung Rye.

In: Journal of Computational Analysis and Applications, Vol. 27, No. 5, 30.10.2019, p. 917-924.

Research output: Contribution to journalArticleResearchpeer-review

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T1 - Additive s-functional inequalities and derivations on Banach algebras

AU - Kim, Taekseung

AU - Jo, Younghun

AU - Park, Junha

AU - Kim, Jaemin

AU - Park, Choonkil

AU - Lee, Jung Rye

PY - 2019/10/30

Y1 - 2019/10/30

N2 - In this paper, we introduce the following new additive s-functional inequalities ||f(x - y) + f(y) + f(-x)II ≤ ||s (f(x + y) - f-x) - f(y)) || (0.1) ||f(x + y) - f-x) - f(y)|| ≤ ||s (f(x - y) + f(y) + f(-x)) ||, (0.2) where s is a _xed complex number with |s| < 1, and prove the Hyers-Ulam stability of linear derivations on Banach algebras associated to the additive s-functional inequalities (0.1) and (0.2).

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