2001, Studia Mathematica 1
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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. -
On the stability of the generalized cosine functional equations
(2001)The aim of this paper is to study the stability problem of the generalized cosine functional equations for complex and vector valued functions. -
On a Banach space automorphism and its connections to functional equations and continuous nowhere differentiable functions
(2001)Denote by $ℋ$ the Banach space of functions $φ : ℝ → ℝ$ which are continuous, 1-periodic and even. It turns out that $F : ℋ → ℋ$, given by \[F[φ](x) := \sum_{k=0}^∞ 1/2^kφ(2^kx),\] is a Banach space automorphism. Important ... -
D'Alembert's functional equation and Chebyshev polynomials
(2001)We consider D’Alembert’s functional equation (1) where the domain of the function $f$ is the additive group of the integers and the codomain is an arbitrary commutative ring with identity. We show that if $f(0) = 1$ then ... -
General continuous solution of a nonlinear functional inequality
(2001)In this paper we present theorems on the existence of continuous solutions of the functional inequality (1) in the case where the continuous solution of the corresponding functional equation (2) is not unique. -
Ternary semigroups of linear mappings and matrices
(2001)Following the classical Green’s equivalences we examine, by means of some equivalence relations, the structure of the ternary semigroup of linear mappings. The suitable results for the ternary semigroup of matrices are ... -
Annales Academiae Paedagogicae Cracoviensis. 4. Studia Mathematica 1
(Wydawnictwo Naukowe Akademii Pedagogicznej, Kraków, 2001)
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