1 - 10 of 19 articles
SummaryThe goal of this paper is to give a survey of all important characterizations of sum form information measures that depend uponk discrete complete probability distributions (without zero probabilities) of lengthn and which satisfy a generalized additivity property. It turns out that most...
SummaryWe give a new simple proof of Šemrl’s recent representation theorem for quasi-quadratic functions acting on unital modules and then show that our approach also gives a certain extension of Šemrl’s result.This paper is intended to point out the usefulness of the ternary point of view even...
SummaryThe purpose of this paper is to present a new approach to smoothness of nonperiodic functions. We consider the space of continuous functions on [−1, 1] as well as the weighted Lp-space and introduce a modulus of smoothness that is based on an algebraic addition ⊕ defined on [−1, 1]. The...
SummaryIn this paper we prove some stability theorems for functional equations of the formg[F(x, y)]=H[g(x), g(y), x, y]. As special cases we obtain well known results for Cauchy and Jensen equations and for functional equations in a single variable.
SummaryThe paper determines all cases when a meromorphic functionF can be expressed both asf ⊗p andf ⊗q with the same meromorphicf and different polynomialsp andq. In all cases there are constantsk, β, a positive integerm, a root λ of unity of orderS and a polynomialr such thatp=(Lr)m+k,q=rm+k,...
SummaryThis note is related to an earlier paper by Bhatia, Davis, and Kittaneh . For matrices similar to Hermitian, we prove an inequality complementary to the one proved in [4, Theorem 3]. We also disprove a conjecture made in  about the norm of a commutator.
SummarySuppose given a quasi-periodic tiling of some Euclidean space Eu which is self-similar under the linear expansiong: Eμ→Eμ. It is known that there is an embedding of Eμ into some higher-dimensional space ℝN and a linear...
SummaryWe produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = ΣI2 =1gl(x)hl(y),x, y∈G, where the functionsf,g1,h1 to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I...
SummaryWe give a survey of known results regarding Schur-convexity of probability distribution functions. Then we prove that the functionF(p1,...,pn;t)=P(X1+...+Xn≤t) is Schur-concave with respect to (p1,...,pn) for every realt, whereXi are independent geometric random variables with...
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