Studia Mathematica: Recent submissions
Wyświetlanie pozycji 181-200 z 206
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The role of nolation in mathematics
(2003)In this paper, the historical development of the Cardan’s rule notation is presented. Some descriptions with respect to the linear and/or structured form of texts are compared, and also the exactness of these descriptions ... -
Annales Academiae Paedagogicae Cracoviensis. 16. Studia Mathematica 3
(Wydawnictwo Naukowe Akademii Pedagogicznej, Kraków, 2003) -
On a paper of T.M.K. Davison
(2002)In his paper the author shows that Chebyshev polynomials of the first kind show up in relation with d’Alembert’s functional equation. Here we point out a similar property of Chebyshev polynomials concerning the square ... -
Some consequences of a theorem of Liouville
(2002)Let $E_n$ denote the $n$-dimensional Euclidean space and $S$ the group of Euclidean similarities. It is shown that the group $ (g, S)$ generated by $S$ and a single diffeomorphism $g$ outside $S$ has an orbit which is dense ... -
Spectra of certain operators and iterative functional equations
(2002)We discuss spectral properties of the operator $F : D -> F|D|$, defined by \[F|ϕ|f(x) := \sum_{k=0}^∞ \frac{1}{2^k}ϕ(2^kx)\] $D$ is the vector space of real functions $ϕ$ such that the sum above converges for all $x ∈ ... -
A proof of S. Rolewicz's conjecture
(2002)S. Rolewicz’s conjecture concerning solutions of the functional-differential inequality (P) is proved. -
Annales Academiae Paedagogicae Cracoviensis. 13. Studia Mathematica 2
(Wydawnictwo Naukowe Akademii Pedagogicznej, Kraków, 2002) -
On a problem of H.-H. Kairies concerning Euler's Gamma function
(2001)The Bohr-Mollerup theorem on the Euler $Γ$ function states: If $f : ℝ_+ → ℝ_+$ satisfies the functional equation $f(x+1) = xf(x)$ on $ℝ_+$, log ○ $f$ is convex on $(γ , +∞)$ for some $γ ≥ 0$ and $f(1) = 1$ then $f = Γ$. ... -
A Wiener Tauberian Theorem on discrete abelian torsion groups
(2001)One version of the classical Wiener Tauberian Theorem states that if $G$ is a locally compact abelian group then any nonzero closed translation invariant subspace of $L^∞(G)$ contains a character. In other words, spectral ... -
On the stability of derivations of higher order
(2001)Derivations of order n as defined by L. Reich are additive and nonlinear functions $f : ℝ → ℝ$ with $f(1) = 0$ which satisfy the functional equation $δ_{a_1}$ ○ $δ_{a_2}$ ○ ... ○ $δ_{a_{(n+1)}}f = 0$ for all $a_1, a_2,..., ... -
On a Pexider type equation on $Δ^+$
(2001)The Pexider equation in question is defined with the use of t-norm and is considered in the space $Δ^+$ of all non decreasing functions $F$ from $ℝ^+$ into $I$ that satisfy $F(0) = 0, F(∞) = 1$ and are left-continuous ... -
Results on the J. d'Alembert equation
(2001)In this paper the authors provide an account of some of their recent results concerning the J. D’Alembert equation especially in a suitable category of noncommutative manifolds. -
Functional and differential equations
(2001)Functional equations play an important role in the theory of differential equations. Euler functional equation for homogeneous functions, Abel and Schroder functional equations and their systems, iteration groups of ... -
Sur quelques problèmes ouverts
(2001)On pose les problèmes au sujet de la raréfaction des ensembles, des prolongements de la mesure de Jordan et des homomorphismes, de la stabilité de l’équation de translation, de la décomposition des fonctions et sur les ... -
Sur les généralisations du wronskien
(2001)En généralisant le wronskien on montre que l’évanouissement de ce wronskien est équivalent à la dépendance linéaire du système des fonc tions. Le théorème analogue est donné pour la décomposition d’une fonc tion $h(x, y)$ ... -
Dynamical interpretation of Schröder's equation. Its consequences
(2001)This text deals with the domain of existence of the solution of Schroder’s equation, related to a two-dimensional real iteration process, defined by functions which do not satisfy the Cauchy-Riemann conditions. Its purpose ... -
Generalized Hosszú functional equations
(2001)Pexiderizations of the Hosszú functional equation \[f(xy) + f(x + y - xy) = f(x) + f(y)\] are considered on a variety of domains.