Jens Schwaiger

STABILITY OF THE MULTI-JENSEN EQUATION

Given an m ∈ N and two vector spaces V and W , a function f : V m → W is called multi-Jensen if it satisfies Jensen’s equation in each variable separately. In this paper we unify these m Jensen equations to obtain a single functional equation for f and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.

Über einen Satz von Shl. Sternberg in der Theorie der analytischen Iterationen

AbstractLet ℂ〚X〛=ℂ〚X1,...,Xn〛 be the ring of formal power series inn indeterminates over ℂ. LetF:X→AX+B(X)=(F(1)(X),...,F(n)(X))∈(ℂ〚X〛)n denote an automorphism of ℂ〚X〛 and let ϱ1,...,ϱn be the eigenvalues of the linear partA ofF. We will say thatF has an analytic iteration (a. i.) if there exists a family (Ft(itX))t∈ℂ of automorphisms such thatFt(X) has coefficients analytic int and such thatF0=X,F1=F,Ft+t′=FtℴFt′ for allt,t′∈ℂ. Let now a setΛ=(lnϱ1,...,lnϱn) of determinations of the logarithms be given. We ask if there exists an a. i. ofF such that the eigenvalues of the linear partA(t) ofFt(X) are

On a characterization of polynomials by divided differences

e^{\ln \varrho _1 t} ,...,e^{\ln \varrho _n t}

On the stability of a system of functional equations characterizing generalized hyperbolic and trigonometric functions

. We will give necessary and sufficient conditions forF to have such an a. i., namely thatF is conjugate to a semicanonical formN=T−1ℴFℴT such that inN(k)(X) there appear at most monomialsX1α1...Xnn

On the Construction of the Field of Reals by Means of Functional Equations and Their Stability and Related Topics

\ln \varrho _k = \sum\limits_{i = 1}^n {\alpha _i \ln } \varrho _i

Linearisierung formal-biholomorpher Abbildungen und Iterationsprobleme

. This generalizes a result of Shl.Sternberg.