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HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, ISSN 1303-5010, 2019, Volume 48, Issue 1, pp. 87 - 101
The estimation of the modulus of algebraic polynomials on the boundary contour with weight function, having some singularities, with respect to the their... 
quasicircle | MATHEMATICS | INEQUALITIES | BEHAVIOR | algebraic polynomials | conformal mapping | STATISTICS & PROBABILITY | INTERFERENCE | BOUNDARY CONTOUR
Journal Article
Filomat, ISSN 0354-5180, 2017, Volume 31, Issue 18, pp. 5647 - 5670
In this work, we investigate the order of the growth of the modulus of orthogonal polynomials over a contour and also arbitrary algebraic polynomials in... 
Algebraic polynomials | Cmooth curve | Conformal mapping | Quasicircle | Orthogonal polynomials | quasicircle | MATHEMATICS | cmooth curve | MATHEMATICS, APPLIED | algebraic polynomials | conformal mapping | BOUNDARY
Journal Article
FILOMAT, ISSN 0354-5180, 2019, Volume 33, Issue 2, pp. 403 - 413
In this study, we give some estimates on the Nikolskii-type inequalities for complex algebraic polynomials in regions with piecewise smooth curves having... 
Bernstein inequalities | quasicircle | MATHEMATICS | MATHEMATICS, APPLIED | Nikol'skii inequalities | INEQUALITIES | conformal mapping | Polynomials
Journal Article
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, ISSN 1370-1444, 04/2016, Volume 23, Issue 2, pp. 285 - 310
In this present work, we continue studying the Bernstein-Walsh type estimations for complex algebraic polynomials in the bounded and unbounded regions with... 
MATHEMATICS | Quasiconformal curve | Polynomials | Conformal mapping | Bernstein-Walsh inequalities | Inequalities (Mathematics) | Research | Mathematical research
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 06/2015, Volume 52, Issue 4, pp. 699 - 725
In this paper, we study the estimation for algebraic polynomials in the bounded and unbounded regions bounded by piecewise Dini smooth curve having interior... 
Conformal mapping | Algebraic polynomials | Dini smooth curve | MATHEMATICS | algebraic polynomials | MATHEMATICS, APPLIED | conformal mapping | CORNERS
Journal Article
Ukrainian Mathematical Journal, ISSN 0041-5995, 10/2014, Volume 66, Issue 5, pp. 645 - 665
Let G ⊂ ℂ be a finite region bounded by a Jordan curve L := ∂G, let Ω : = e x t G ¯ $$ \Omega :=\mathrm{e}\mathrm{x}\mathrm{t}\overline{G} $$ (with respect to... 
Geometry | Algebra | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Statistics, general | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Ukrainian Mathematical Journal, ISSN 0041-5995, 03/2017, Volume 68, Issue 10, pp. 1574 - 1590
We study the order of height for the modulus of arbitrary algebraic polynomials with respect to weighted Lebesgue spaces in which the contour and weight... 
MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX-PLANE | INEQUALITIES | Functions (mathematics) | Shape | Algebra | Singularities | Mathematical analysis | Contours | Polynomials
Journal Article
Ukrainian Mathematical Journal, ISSN 0041-5995, 08/2018, Volume 70, Issue 3, pp. 362 - 384
We study the order of growth of the moduli of arbitrary algebraic polynomials in the weighted Bergman space A(p)(G, h), p > 0, in regions with zero interior... 
MATHEMATICS | MATHEMATICS, APPLIED | UNIFORM | BEHAVIOR | SMOOTH BOUNDARY | COMPLEX-PLANE | ORTHOGONAL POLYNOMIALS | WEIGHT | Polynomials | Algebra | Smooth boundaries
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2017, Volume 11, Issue 7, pp. 1569 - 1586
In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and the... 
30C10 | Operator Theory | Primary 30A10 | Conformal mapping | Analysis | Mathematics, general | Mathematics | Algebraic polynomials | Orthonormal polynomials | Quasicircle | Secondary 41A17 | MATHEMATICS | MATHEMATICS, APPLIED | ORTHOGONAL POLYNOMIALS | COMPLEX-PLANE | BOUNDARY | Functions (mathematics) | Shape | Singularities | Mathematical analysis | Contours | Inequalities | Polynomials
Journal Article
Ukrainian Mathematical Journal, ISSN 0041-5995, 10/2017, Volume 69, Issue 5, pp. 675 - 695
We continue our investigation of the Nikol’skii and Bernstein–Walsh-type estimations for complex algebraic polynomials in the bounded and unbounded quasidisks... 
Geometry | Algebra | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Statistics, general | MATHEMATICS | MATHEMATICS, APPLIED | HOLDER CONTINUITY | CONFORMAL-MAPS | BEHAVIOR | SMOOTH BOUNDARY | REGIONS | COMPLEX-PLANE | ORTHOGONAL POLYNOMIALS | Polynomials
Journal Article
Annales Polonici Mathematici, ISSN 0066-2216, 2014, Volume 111, Issue 1, pp. 39 - 58
We continue studying the estimation of Bernstein-Walsh type for algebraic polynomials in regions with piecewise smooth boundary. 
Quasiconformal curve | Algebraic polynomials | Conformal mapping | Smooth curve | MATHEMATICS | algebraic polynomials | conformal mapping | smooth curve | ORTHOGONAL POLYNOMIALS | quasiconformal curve
Journal Article
Journal of Inequalities and Applications, ISSN 1029-242X, 05/2010, Volume 2010, Issue 1, pp. 716176 - 716176
The aim of this paper is to investigate approximation properties of some extremal polynomials in , space. We are interested in finding approximation rate of... 
Journal Article
Science China Mathematics, ISSN 1674-7283, 5/2015, Volume 58, Issue 5, pp. 1063 - 1078
Let G ⊂ ℂ be a simply connected domain whose boundary L := ∂G is a Jordan curve and 0 ∈ G. Let w = φ(z) be the conformal mapping of G onto the disk B(0, r 0)... 
30E10 | Bieberbach polynomials | 30C30 | quasiconformal curve | complex approximation | conformal mapping | Mathematics | 30C70 | Applications of Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | REGIONS | BOUNDARY | Conformal mapping | Mathematical analysis | Exteriors | China | Disks | Polynomials | Boundaries | Convergence
Journal Article
Ukrainian Mathematical Journal, ISSN 0041-5995, 7/2018, Volume 70, Issue 2, pp. 165 - 181
We study the possibility of application of Faber polynomials in proving some combinatorial identities. It is shown that the coefficients of Faber polynomials... 
Geometry | Algebra | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Statistics, general | MATHEMATICS | MATHEMATICS, APPLIED | Thermal expansion | Polynomials | Combinatorial analysis
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2011, Volume 36, Issue 1, pp. 353 - 392
We find necessary and sufficient conditions for an arbitrary metric space X to have a unique pretangent space at a marked point a is an element of X. Applying... 
Cantor set | Metric spaces | Pretangent spaces | Logarithmic spiral | Uniqueness of pretangent metric spaces | MATHEMATICS | pretangent spaces | SOBOLEV SPACES | SETS | logarithmic spiral | uniqueness of pretangent metric spaces
Journal Article
Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 07/2013, Volume 14, Issue 3, pp. 551 - 581
Let A subset of C be a starlike set with a center a. We prove that every tangent space to A at the point a is isometric to the smallest closed cone, with the... 
Metric spaces | Tangent space to starlike sets | Tangent spaces to metric spaces | Tangent space to convex sets | MATHEMATICS | MATHEMATICS, APPLIED | tangent space to starlike sets | SOBOLEV SPACES | tangent spaces to metric spaces | tangent space to convex sets
Journal Article
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, ISSN 1521-1398, 01/2004, Volume 6, Issue 1, pp. 43 - 59
In this work the order of the height of orthogonal polynomials over the region with respect to the weight is analized, when the boundary contour and the weight... 
quasicircle | MATHEMATICS, APPLIED | weight function | conformal mapping | COMPUTER SCIENCE, THEORY & METHODS | quasiconformal mapping | orthogonal polynomials
Journal Article
Ukrainian Mathematical Journal, ISSN 0041-5995, 8/2011, Volume 63, Issue 3, pp. 337 - 350
Let $$ G \subset {\mathbb C} $$ be a finite region bounded by a Jordan curve $$ L: = \partial G $$ , let $$ \Omega : = {\text{ext}}\bar{G} $$ (with respect to... 
Geometry | Algebra | Analysis | Mathematics, general | Mathematics | Statistics, general | Applications of Mathematics | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Bulletin of the Belgian Mathematical Society - Simon Stevin, ISSN 1370-1444, 04/2009, Volume 16, Issue 2, pp. 235 - 250
The order of the weight of orthogonal polynomials is analyzed, when this weight function shows singularities on the boundary of a region in the complex plane. 
Quasiconformal mapping | Conformal mapping | Weight function | Quasicircle | Orthogonal polynomials | MATHEMATICS | CONTOUR | Polynomials | Quasiconformal mappings | Analysis | Functions, Orthogonal | 30C10 | 30A10 | 41A17
Journal Article
Journal of Endourology, ISSN 0892-7790, 09/2017, Volume 31, Issue S2, pp. P1 - A474
Journal Article
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