http://hdl.handle.net/11716/5430 2026-04-09T02:37:26Z http://hdl.handle.net/11716/5453 Report of Meeting - 7th International Conference on Functional Equations and Inequalities, Zlockie, September 12-18,1999 Choczewski, Bogdan 2001-01-01T00:00:00Z http://hdl.handle.net/11716/5452 On a problem of H.-H. Kairies concerning Euler's Gamma function Wach-Michalik, Anna 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 $f = Γ$. We give some partial answers to the question posed by H.-H. Kairies: By what other function can the logarithm be replaced in this statement. 2001-01-01T00:00:00Z http://hdl.handle.net/11716/5451 A Wiener Tauberian Theorem on discrete abelian torsion groups Székelyhidi, László 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 analysis holds for $L^∞(G)$. In this paper we prove a similar theorem: if $G$ is a discrete abelian torsion group then spectral analysis holds for $C(G)$, the space of all complex valued functions on $G$. 2001-01-01T00:00:00Z http://hdl.handle.net/11716/5450 On the stability of derivations of higher order Schwaiger, Jens 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 $a_1, a_2,..., a_{n+1} ϵ ℝ$, where $δ_af(x) := f(ax) - af(x)$. Here we prove several stability results concerning this (and similar) functional equations. 2001-01-01T00:00:00Z