Milan Merkle

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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)
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)
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)
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)
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