We propose a method, based on logarithmic convexity, for producing sharp Ž. Ž. bounds for the ratio ⌫ x q ␤ r⌫ x. As an application, we present an inequality that sharpens and generalizes inequalities due It is well known that the second derivative of the function x ¬ log ⌫ x Ž w x w x. can be expressed in terms of the series see 2 or 10 d 2 1 1 1 log ⌫ x s… (More)
We consider the ratio T(x,y) = r(~)r(y)/r2((~ + y)/2) and its properties related to convexity, logarithmic convexity, Schur-convexity, and complete monotonicity. Several new bounds and asymptotic expansions for T are derived. Sharp bounds for the function x ~-~ x/(1-e-~) are presented, as well as bounds for the trigamma function. The results axe applied to… (More)
The first part of the paper deals with general features of weak star convergence from a topological point of view. We present basic facts about weak and weak star topologies, dual spaces and representations of linear functionals as Radon measures. A special attention is payed to finitely additive measures and some results regarding the Baire sets. We prove… (More)
We prove the existence of a solution to the generalized vector equilibrium problem with bounds. We show that several known theorems from the literature can be considered as particular cases of our results, and we provide examples of applications related to best approximations in normed spaces and variational inequalities.
We present a new algorithm for Tukey (halfspace) depth level sets and its implementation. Given d-dimensional data set for any d ≥ 2, the algorithm is based on representation of level sets as intersections of balls in R d , and can be easily adapted to related depths (Type D, Zuo and Serfling (Ann. Stat. 28 (2000), 461–482)). The algorithm complexity is… (More)
The Barnes' G-function G(x) = 1/Γ2, satisfies the functional equation log G(x + 1) − log G(x) = log Γ(x). We complement W. Krull's work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = ϕ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on… (More)
This is the last issue of the journal Publikacije Elektrotehničkog Fakulteta-serija Matematika (PEF), or with the English title, Publications of the Faculty of Electrical Engineering-series Mathematics. Founded in the year 1956 as Serija Matematika i Fizika, the journal will continue its life under the name Applicable Analysis and Discrete Mathematics… (More)
More than a century ago, G. Kowalewski stated that for each n continuous functions on a compact interval [a, b], there exists an n-point quad-rature rule (with respect to Lebesgue measure on [a, b]), which is exact for given functions. Here we generalize this result to continuous functions with an arbitrary positive and finite measure on an arbitrary… (More)