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pro vyhledávání: '"Aserrar, Youssef"'
Autor:
Aserrar, Youssef, Elqorachi, Elhoucien
Let $S$ be a semigroup, $Z(S)$ the center of $S$ and $\sigma:S\rightarrow S$ is an involutive automorphism. Our main results is that we describe the solutions of the Kannappan-Wilson functional equation \[\displaystyle \int_{S} f(xyt)d\mu(t) +\displa
Externí odkaz:
http://arxiv.org/abs/2405.03835
Autor:
Aserrar Youssef, Elqorachi Elhoucien
Publikováno v:
Annales Mathematicae Silesianae, Vol 38, Iss 2, Pp 155-176 (2024)
Let S be a semigroup. Our main results are that we describe the complex-valued solutions of the following functional equations g(xσ(y))=g(x)g(y)+f(x)f(y),x,y∈S,f(xσ(y))=f(x)g(y)+f(y)g(x),x,y∈S,\matrix{ {g\left( {x\sigma \left( y \right)} \right
Externí odkaz:
https://doaj.org/article/1f5fb897176640f094429ca80e6cb473
Autor:
Aserrar, Youssef, Elqorachi, Elhoucien
Let $S$ be a semigroup. Our main results is that we describe the complex-valued solutions of the following functional equations \[g(x\sigma (y)) = g(x)g(y)+f(x)f(y),\ x,y\in S,\] \[f(x\sigma (y)) = f(x)g(y)+f(y)g(x),\ x,y\in S,\] and \[f(x\sigma (y))
Externí odkaz:
http://arxiv.org/abs/2302.10263
We determine the complex-valued solutions of the following functional equation \[f(xy)+\mu (y)f(\sigma (y)x) = 2f(x)g(y),\quad x,y\in S,\] where $S$ is a semigroup and $\sigma$ an automorphism, $\mu :S\rightarrow \mathbb{C}$ is a multiplicative funct
Externí odkaz:
http://arxiv.org/abs/2210.09939
Autor:
Aserrar, Youssef, Elqorachi, Elhoucien
We treat two related trigonometric functional equations on semigroups. First we solve the $\mu$-sine subtraction law \[\mu(y) k(x \sigma(y))=k(x) l(y)-k(y) l(x), \quad x, y \in S,\] for $k, l : S\rightarrow \mathbb{C}$, where $S$ is a semigroup and $
Externí odkaz:
http://arxiv.org/abs/2210.09111
Autor:
Aserrar, Youssef, Elqorachi, Elhoucien
Our main result is that we describe the solutions $g,f:S\rightarrow\mathbb{C}$ of the functional equation \[g(x\sigma(y))=g(x)g(y)-f(x)f(y)+\alpha f(x\sigma(y)),\quad x,y\in S,\] where $S$ is a semigroup, $\alpha \in \mathbb{C}$ is a fixed constant a
Externí odkaz:
http://arxiv.org/abs/2210.08133
Autor:
Aserrar, Youssef, Elqorachi, Elhoucien
In this paper, we determine the complex-valued solutions of the following functional equations \[g(x\sigma (y)) = g(x)g(y)+f(x)f(y),\quad x,y\in S,\]\[f(x\sigma (y)) = f(x)g(y)+f(y)g(x),\quad x,y\in S,\]\[f(x\sigma (y)) = f(x)g(y)+f(y)g(x)-g(x)g(y),\
Externí odkaz:
http://arxiv.org/abs/2210.06181
Akademický článek
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Publikováno v:
International Journal of Nonlinear Analysis & Applications; Nov2024, Vol. 15 Issue 11, p403-415, 13p
Autor:
Aserrar, Youssef1 (AUTHOR) youssefaserrar05@gmail.com, Elqorachi, Elhoucien1 (AUTHOR)
Publikováno v:
Aequationes Mathematicae. Aug2023, Vol. 97 Issue 4, p787-804. 18p.