| Autor: |
Ebanks Bruce |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
Annales Mathematicae Silesianae, Vol 36, Iss 1, Pp 30-52 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2391-4238 |
| DOI: |
10.2478/amsil-2021-0012 |
| Popis: |
The primary object of study is the “cosine-sine” functional equation f(xy) = f(x)g(y)+g(x)f(y)+h(x)h(y) for unknown functions f, g, h : S → ℂ, where S is a semigroup. The name refers to the fact that it contains both the sine and cosine addition laws. This equation has been solved on groups and on semigroups generated by their squares. Here we find the solutions on a larger class of semigroups and discuss the obstacles to finding a general solution for all semigroups. Examples are given to illustrate both the results and the obstacles. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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