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Abstract. 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 quadrature 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… (More)

- Milan Merkle
- 2009

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)

- Zoran D. Mitrovic, Milan Merkle
- Appl. Math. Lett.
- 2010

(1) x0 ∈ K such that c1 ≤ f(x0, y) ≤ c2, for all y ∈ K, where K is a given set, f : K × K → R is a given function and c1 and c2 two real numbers such that c1 ≤ c2. If K is a nonempty closed subset in a locally convex semi-reflexive topological vector space, then the problem (1) is problem by Isac, Sehgal and Singh [16] (Open Problem 2). In [20], Li gave the… (More)

- Milan Merkle
- International Encyclopedia of Statistical Science
- 2011

- Milos Bjelic, Miodrag Stanojevic, Jelena D. Certic, Milan Merkle
- IET Circuits, Devices & Systems
- 2017

- Milan Merkle
- International Encyclopedia of Statistical Science
- 2011

- Milica Bogicevic, Milan Merkle
- ArXiv
- 2016

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, and can be easily adapted to related depths (Type D, Zuo and Serfling (Ann. Stat. 28 (2000), 461–482)). The algorithm complexity is O(dn +… (More)

- Milan Merkle
- 2007

S OF TALKS PRESENTED AT THE INTERNATIONAL<lb>MATHEMATICAL CONFERENCE TOPICS IN MATHEMATICAL ANALYSIS<lb>AND GRAPH THEORY (MAGT) A Satellite Meeting to ICM 2006 BELGRADE, SERBIA, SEPTEMBER 1–4, 2006. Editorial note. Selected peer-refereed full presented at MAGT 2006, are published<lb>in: Applicable Analysis and Discrete Mathematics, 1, No. 1 (2007).

- Milan Merkle, Monica Moulin Ribeiro Merkle
- Applied Mathematics and Computation
- 2011

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)

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