A trigonometric functional equation with an automorphism | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 30، دوره 15، شماره 11، بهمن 2024، صفحه 403-415 اصل مقاله (384.64 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31988.4745 | ||
| نویسندگان | ||
| Youssef Aserrar* 1؛ Elhoucien Elqorachi1؛ Th.M. Rassias2 | ||
| 1Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Agadir, Morocco | ||
| 2Department of Mathematics, National Technical University of Athens, Athens, Greece | ||
| چکیده | ||
| Let $S$ be a semigroup. In the present paper, we determine the complex-valued solutions $(f,g)$ of the functional equation $$g(x\sigma (y)) = g(x)g(y)-f(x)f(y)+\alpha f(x\sigma(y)),\ x,y\in S,$$ where $\sigma :S\rightarrow S$ is an automorphism that need not be involutive, and $\alpha \in \mathbb{C}$ is a fixed constant. Our results generalize and extend the ones by Stetk\ae r in The cosine addition law with an additional term. Aequat Math., no. 6, 90, 1147-1168 (2016), and also the ones by Aserrar and Elqorachi in A generalization of the cosine addition law on semigroups. Aequat Math. 97, 787–804 (2023). Some consequences of our results are presented. | ||
| کلیدواژهها | ||
| Functional equation؛ Semigroup؛ Addition law؛ Automorphism | ||
| مراجع | ||
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