Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Elqorachi Elhoucien"'
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, $Z(S)$ 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:
Elqorachi Elhoucien, Redouani Ahmed
Publikováno v:
Annales Mathematicae Silesianae, Vol 32, Iss 1, Pp 169-200 (2018)
We study the solutions of the integral Kannappan’s and Van Vleck’s functional equations ∫Sf(xyt)dµ(t)+∫Sf(xσ(y)t)dµ(t)= 2f(x)f(y), x,y ∈ S; ∫Sf(xσ(y)t)dµ(t)-∫Sf(xyt)dµ(t)= 2f(x)f(y), x,y ∈ S; where S is a semigroup, σ is an inv
Externí odkaz:
https://doaj.org/article/693d240a90744b8bb069b3deec857064
Let $S$ be a semigroup, $z_0$ a fixed element in $S$ and $\sigma:S \longrightarrow S$ an involutive automorphism. We determine the complex-valued solutions of Kannappan-sine subtraction law $f(x\sigma(y)z_0)=f(x)g(y)-f(y)g(x),\; x,y \in S$. As an app
Externí odkaz:
http://arxiv.org/abs/2401.06147
Autor:
Ajebbar, Omar, Elqorachi, Elhoucien
Let $S$ be a semigroup. We determine the complex-valued solutions $f,g,h$ of the functional equation \begin{equation*}f(xy)=f(x)g(y)+g(x)f(y)+h(x)h(y), x,y\in S,\end{equation*} in terms of multiplicative functions, solutions of the special case $$\va
Externí odkaz:
http://arxiv.org/abs/2306.04666
We determine the complex-valued solutions of the Kannappan cosine functional law $g(xyz_{0})=g(x)g(y)-f(x)f(y)$, $x,y\in S$, where $S$ is a semigroup and $z_{0}$ is a fixed element in $S.$
Externí odkaz:
http://arxiv.org/abs/2305.02924
Let $S$ be a semigroup and $z_{0}$ a fixed element in $S.$ We determine the complex-valued solutions of the following Kannappan-sine addition law $f(xyz_{0})=f(x)g(y)+f(y)g(x),x,y\in S.$
Externí odkaz:
http://arxiv.org/abs/2304.14146
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