Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06147 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909070884077568 |
|---|---|
| author | Jafar, Ahmed Ajebbar, Omar Elqorachi, Elhoucien |
| author_facet | Jafar, Ahmed Ajebbar, Omar Elqorachi, Elhoucien |
| contents | Let $S$ be a semigroup, $z_0$ a fixed element in $S$ and $σ:S \longrightarrow S$ an involutive automorphism. We determine the complex-valued solutions of Kannappan-sine subtraction law $f(xσ(y)z_0)=f(x)g(y)-f(y)g(x),\; x,y \in S$. As an application we solve the following variant of Kannappan-sine subtraction law viz. $f(xσ(y)z_0)=f(x)g(y)-f(y)g(x)+λg(xσ(y)z_0) ,\; x,y \in S,$ where $λ\in \mathbb{C}^{*}$. The continuous solutions on topological semigroups are given and an example to illustrate the main results is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06147 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Kannappan-sine subtraction law on semigroups Jafar, Ahmed Ajebbar, Omar Elqorachi, Elhoucien General Mathematics Let $S$ be a semigroup, $z_0$ a fixed element in $S$ and $σ:S \longrightarrow S$ an involutive automorphism. We determine the complex-valued solutions of Kannappan-sine subtraction law $f(xσ(y)z_0)=f(x)g(y)-f(y)g(x),\; x,y \in S$. As an application we solve the following variant of Kannappan-sine subtraction law viz. $f(xσ(y)z_0)=f(x)g(y)-f(y)g(x)+λg(xσ(y)z_0) ,\; x,y \in S,$ where $λ\in \mathbb{C}^{*}$. The continuous solutions on topological semigroups are given and an example to illustrate the main results is also given. |
| title | A Kannappan-sine subtraction law on semigroups |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2401.06147 |