Rocznik Naukowo-Dydaktyczny: Recent submissions
Now showing items 41-60 of 3302
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Remarks on quasi-arithmetic means
(2000) -
Ring homomorphisms equation revisited
(2000)The functional equation f(x + y) + f(xy) = f{x) + f(y) + f(x)f(y) (*) has been studied by J. Dhombres (Relations de dépendance entre les équations fonctionnelles de Cauchy, Aequationes Math. 35 (1988), 186- 212) for ... -
Matkowski-Sutô type problem for conjugate arithmetic means
(2000)Let I ⊂ R be an open interval and let CM(I) denote the set of all continuous and strictly monotonie real functions on I. For ϕ ϵ CM(I) we define A[*][ϕ](x,y) := ϕ[-1](ϕ(x) + ϕ(y) - ϕ(x+y/2) for all x,y ϵ I, which is ... -
The rotation number of the composition of homeomorphisms
(2000)In this paper it is shown that if F and G are commuting orientation-preserving homeomorphisms of the unit circle, then α(F ◦ G) = α(F) + α(G) (mod 1), where α(F) denotes the rotation number of F. -
A functional inequality related to Böttcher’s equation
(2000)There is proved a theorem on the form of continuous solutions of the iterative functional inequality (1) in the case where the function f in (1) possesses an asymptotic property at the origin. The formula we present ... -
Note on some functional equations of Gołąb-Schinzel type
(2000)In the present paper, we consider the following functional equation of Gołąb-Schinzel type: f(f(x)[n]y + f(y)[k]x) = ф(f(х), f(y)) (1) where ф : R[2] → R is a given function, f : E → R is the unknown function, E ... -
Characterization of transformed linear functions via shift invariances
(2000)Transforms of linear functions in two variables are characterized via translation like composite functional equations on restricted domain, under regularity assumptions of C[1] type. -
DeSitter distances in Hilbert spaces
(2000)All 2-point invariants of an arbitrary DeSitter manifold are determined without any regularity assumption, especially those which are additive on geodesics. -
An alternative Cauchy equation almost everywhere
(2000)Let (S, +) be a commutative semigroup and let ζ be a proper left translation invariant σ-ideal in S. Suppose that f : S → R satisfies |f(x + y)| = |f(x) + f(y)| Ω(ζ)-almost everywhere in S x S. We prove that there exists, ... -
On decent solutions of a functional congruence
(2000)A Cauchy functional congruence and corresponding characters are discussed from the point of view of decency in the sense of Baker. -
On some inequalities related to Cauchy-Schwarz inequality
(2000)Using some results of functional equations we solve some inequalities in real normed spaces of dimension 2 and 3 which generalize the classical Cauchy-Schwarz inequality and which characterize Some special norms -
A couple of functional equations applied to utility theory
(2000)We show how characterizations of separable and additive representations of rank-dependent expected utility and of rank- independent expected utility lead to the functional equation f(v) = f(vw) + f(g-1[g(v)q(w)]) (v ϵ ... -
Rocznik Naukowo-Dydaktyczny. Z. 204. Prace Matematyczne 17
(Wydawnictwo Naukowe Akademii Pedagogicznej, Kraków, 2000)The year 2000 is the year of a double jubilee of Prof. Dr. Zenon Moszner: the 70th anniversary of his birthday and the 50th year of his work at the Pedagogical University of Kraków. The present special volume of the Rocznik ... -
On a functional equation of Abel
(1999)We are concerned with the general solution and the stability problem for the functional equation f(x + y) = g(xy) + h(x - y) in the case f,g,h : [0, ∞) -> S, where S is an Abelian semigroup with the cancelation law. The ... -
Concave itération semigroups of Jensen set-valued functions
(1999)Let S be a closed convex cone such that int S ≠ 0 in a real separable Banach space. A necessary and sufficient condition is given under which a family {F[t] : t ≥ 0} of set-valued functions F[t] : S -> cc(S) is a concave ... -
L’équation de translation et l’équation de Sincov généralisée
(1999)On donne une liaison entre l’équation de translation (1) et l’équation de Sincov généralisée (2), aussi dans le cas du type de Pexider ((20) et (23)). On formule aussi quelques problèmes ouverts.