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pro vyhledávání: '"39B52"'
In this paper, we investigate some hyperstability results, inspired by the concept of Ulam stability, for the following functional equations: \begin{equation} \varphi(x+y)+\varphi(x-y)=2\varphi(x)+2\varphi(y) \end{equation} \begin{equation} \varphi(a
Externí odkaz:
http://arxiv.org/abs/2410.09082
Autor:
Daianu, Dan M
Using the section method we characterize the solutions $ f:U\rightarrow Y$ of the following four equations \begin{equation*} \sum\limits_{i=0}^{n}\left( -1\right) ^{n-i}\tbinom{n}{i}f\left( \sqrt[m]{ u^{m}+iv^{m}}\right) =\left( n!\right) f\left( v\r
Externí odkaz:
http://arxiv.org/abs/2409.11204
Autor:
Baza, Abderrahman, Rossafi, Mohamed
In this work, we prove the generalised Hyer Ulam stability of the following functional equation \begin{equation}\label{Eq-1} \phi(x)+\phi(y)+\phi(z)=q \phi\left(\sqrt[s]{\frac{x^s+y^s+z^s}{q}}\right),\qquad |q| \leq 1 \end{equation} and $s$ is an odd
Externí odkaz:
http://arxiv.org/abs/2408.10225
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of functional and fun
Externí odkaz:
http://arxiv.org/abs/2407.08079
This study extends the functional perturbation theory~(FPT) of dynamical systems, which was initially developed for investigating the shifts of magnetic field line trajectories within the chaotic edge region of plasma when subjected to global perturb
Externí odkaz:
http://arxiv.org/abs/2407.06440
Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control, are computa
Externí odkaz:
http://arxiv.org/abs/2407.06430
Using the direct method, we prove the generalised Hyers-Ulam stability of the following functional equation \begin{equation} \phi(x+y, z+w)+\phi(x-y, z-w)-2 \phi(x, z)-2 \phi(x, w)=0 \end{equation} in modular space satisfying the Fatou property or $\
Externí odkaz:
http://arxiv.org/abs/2406.15436
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:
Feldman, Gennadiy
By the well-known I.Kotlarski lemma, if $\xi_1$, $\xi_2$, and $\xi_3$ are independent real-valued random variables with nonvanishing characteristic functions, $L_1=\xi_1-\xi_3$ and $L_2=\xi_2-\xi_3$, then the distribution of the random vector $(L_1,
Externí odkaz:
http://arxiv.org/abs/2404.10916
Publikováno v:
Open Mathematics, Vol 22, Iss 1, Pp 263-279 (2024)
Using the direct method, we prove the Hyers-Ulam-Rassias stability of the following functional equation: ϕ(x+y,z+w)+ϕ(x−y,z−w)−2ϕ(x,z)−2ϕ(x,w)=0\phi \left(x+y,z+w)+\phi \left(x-y,z-w)-2\phi \left(x,z)-2\phi \left(x,w)=0 in ρ\rho -complet
Externí odkaz:
https://doaj.org/article/fb83ca425f4f4e1189e17e812c3ec5c0
