Dušan Lj. Djukić

University of Belgrade · Faculty of Mechanical Engineering

Ageneralization of the deeply investigated harmonic functions, known as ?-harmonic functions, have recently gained considerable attention. Similarly to the harmonic functions, an ?-harmonic function u on the unit disc D is uniquely determined by its values on the boundary of the disc ?D. In fact, for any z ? D, the value of u(z) can be given as a c...

Stratified cubature rules are proposed to approximate double integrals defined on the real positive semiaxis. In particular, anti-Gauss cubature formulae are introduced and averaged cubature schemes are developed. Some of their appropriate modifications are also studied. Several numerical experiments are given to testify the performance of all the...

Gauss quadrature rules are commonly used to approximate integrals determined by a measure with support on a real interval. These rules are known to be internal, i.e., their nodes are in the convex hull of the support of the measure. This allows the application of Gauss rules also when the integrand only is defined on the convex hull of the support...

It is desirable that a quadrature rule be internal, i.e., that all nodes of the rule live in the convex hull of the support of the measure. Then the rule can be applied to approximate integrals of functions that have a singularity close to the convex hull of the support of the measure. This paper investigates whether generalized averaged Gauss quad...

Generalized averaged Gaussian quadrature rules and truncated variants associated with a nonnegative measure with support on a real open interval {t:a<t<b} may have nodes outside this interval, in other words the rules may fail to be internal. Such rules cannot be applied when the integrand is defined on {t:a<t<b} only. This paper investigates wheth...

Generalized averaged Gaussian quadrature rules associated with some measure, and truncated variants of these rules, can be used to estimate the error in Gaussian quadrature rules. However, the former quadrature rules may have nodes outside the interval of integration and, therefore, it may not be possible to apply them when the integrand is defined...

We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szegő weight functions consisting of any one of the four Chebyshev weights divided by the polynomial (Formula presented.). For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on e...

Generalized averaged Gaussian quadrature formulas may yield higher accuracy than Gauss quadrature formulas that use the same moment information. This makes them attractive to use when moments or modified moments are cumbersome to evaluate. However, generalized averaged Gaussian quadrature formulas may have nodes outside the convex hull of the suppo...

Generalized averaged Gauss quadrature formulas may have nodes outside the interval of integration. Quadrature rules with nodes outside the interval of integration cannot be applied to approximate integrals with an integrand that is defined on the interval of integration only. This paper investigates when generalized averaged Gauss quadrature rules...

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

The following is a list of the most basic concepts and theorems frequently used in this book. We encourage the reader to become familiar with them and perhaps read up on them further in other literature.

The desired result\((14n + 3,21n + 4) = 1 follows from 3(14n+3) - 2(21n+4) = 1. \)

The International Mathematical Olympiad (IMO) is the most important and prestigious mathematical competition for high-school students. It has played a significant role in generating wide interest in mathematics among high school students, as well as identifying talent.

Problem Books in Mathematics The IMO CompendiumA Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2004 10.1007/0-387-33430-0_3 DušanDjukić, VladimirJanković, IvanMatić and NikolaPetrović 3.Problems