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pro vyhledávání: '"39b22"'
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:
Kiss, Tibor, Nagy, Gergő
The aim of this paper is to characterize the so-called $\sigma$-balancing property in the class of generalized quasi-arithmetic means. In general, the question is whether those elements of a given family of means that possess this property are quasi-
Externí odkaz:
http://arxiv.org/abs/2405.08583
Iverson (2006) proposed the law of similarity \[ \xi_{s}(\lambda x)= \gamma(\lambda, s)\xi_{\eta(\lambda, s)}(x) \] for the sensitivity functions $\xi_{s}\, (s\in S)$. Compared to the former models, the generality of this one lies in that here $\gamm
Externí odkaz:
http://arxiv.org/abs/2402.07670
Autor:
Jarczyk, Witold, Pasteczka, Paweł
Given a set $T \subset (0, +\infty)$, intervals $I\subset (0, +\infty)$ and $J\subset {\mathbb R}$, as well as functions $g_t:I\times J\rightarrow J$ with $t$'s running through the set \[ T^{\ast}:=T \cup \big\{t^{-1}\colon t \in T\big\}\cup\{1\} \]
Externí odkaz:
http://arxiv.org/abs/2311.09927
Autor:
Fechner, Włodzimierz, Gselmann, Eszter
The paper aims to provide a full characterization of all operators $T\colon \mathscr{P}(\mathbb{C}) \to \mathscr{P}(\mathbb{C})$ acting on the space of all complex polynomials that satisfy the Leibniz rule \[ T(f\cdot g)= T(f)\cdot g+f\cdot T(g) \] f
Externí odkaz:
http://arxiv.org/abs/2311.04671
Autor:
Glavosits T., Karácsony Zs.
Publikováno v:
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 32, Iss 3, Pp 89-102 (2024)
Let Y (+) be a group, D ⊆ ℤ2 where ℤ(+, ⩽) denotes the ordered group of all integers, and ℤ2 := ℤ×ℤ. We shall use the notations Dx := {u ∈ ℤ | ∃v ∈ X : (u, v) ∈ D}, Dy := {v ∈ ℤ | ∃u ∈ ℤ : (u, v) ∈ D}, Dx+y := {z
Externí odkaz:
https://doaj.org/article/251c3dc39f9b465d97c7c536bca45e28
Let $r$ be a positive integer, $N$ be a nonnegative integer and $\Omega \subset \mathbb{R}^{r}$ be a domain. Further, for all multi-indices $\alpha \in \mathbb{N}^{r}$, $|\alpha|\leq N$, let us consider the partial differential operator $D^{\alpha}$
Externí odkaz:
http://arxiv.org/abs/2309.03572
{Let $N, k$ be positive integers with $k\geq 2$, and $\Omega \subset \mathbb{R}^{N}$ be a domain.} By the well-known properties of the Laplacian and the gradient, we have \[ \Delta(f\cdot g)(x)=g(x) \Delta f(x)+f(x) \Delta g(x)+2\langle \nabla f(x),
Externí odkaz:
http://arxiv.org/abs/2306.02788
Autor:
Bauer, Benedict, Gerhold, Stefan
We characterize all real matrix semigroups satisfying a mild boundedness assumption, without assuming continuity. Besides the continuous solutions of the semigroup functional equation, we give a description of solutions arising from non-measurable so
Externí odkaz:
http://arxiv.org/abs/2305.15522
Autor:
Farhi, Bakir
The purpose of the present paper is to show that in certain classes of real (or complex) functions, the Bernoulli polynomials are essentially the only ones satisfying the Raabe functional equation. For the class of the real $1$-periodic functions whi
Externí odkaz:
http://arxiv.org/abs/2303.14492