### 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 language | English |
---|---|

Pages (from-to) | 917-924 |

Number of pages | 8 |

Journal | Journal of Computational Analysis and Applications |

Volume | 27 |

Issue number | 5 |

State | Published - 2019 Oct 30 |

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### Keywords

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

### Cite this

*Journal of Computational Analysis and Applications*,

*27*(5), 917-924.

}

*Journal of Computational Analysis and Applications*, vol. 27, no. 5, pp. 917-924.

**Additive s-functional inequalities and derivations on Banach algebras.** / Kim, Taekseung; Jo, Younghun; Park, Junha; Kim, Jaemin; Park, Choonkil; Lee, Jung Rye.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

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).

AB - 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).

KW - Additive s-functional inequality

KW - Derivation on Banach algebra

KW - Direct method

KW - Hyers-Ulam stability

UR - http://www.scopus.com/inward/record.url?scp=85045526439&partnerID=8YFLogxK

M3 - Article

VL - 27

SP - 917

EP - 924

JO - Journal of Computational Analysis and Applications

JF - Journal of Computational Analysis and Applications

SN - 1521-1398

IS - 5

ER -