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İç ve Dış Sıfır Açılı Bölgelerde Polinom için Düzgün ve Noktasal Değerlendirmeler

Yıl 2018, Cilt: 39 Sayı: 1, 47 - 65, 16.03.2018

Pelin Özkartepe

https://doi.org/10.17776/csj.405512
Cited By: 4

Öz

Bu
çalışmada, içte ve dışta sıfır açı olan parçalı Dini düzgün eğri ile sınırlı
sonlu ve sonsuz bölgelerdeki cebirsel polinomlar için düzgün ve noktasal
değerlendirmeler inceledik.

Anahtar Kelimeler

Cebirsel polinomlar

Kaynakça

  • [1] Abdullayev F.G., Andrievskii V.V. On the orthogonal polynomials in the domains with -quasiconformal boundary. Izv. Akad. Nauk Azerb. SSR., Ser. FTM 1983; 1: 3-7.
  • [2] Abdullayev F. G., Özkartepe N. P., Gün C. D. Uniform and pointwise polynomial inequalities in regions without cusps in the weighted Lebesgue space. Bulletin of Tbilisi ICMC , 18-1 (2014) 146-167.
  • [3] Abdullayev F.G., Özkartepe P. On the growth of algebraic polynomials in the whole complex plane. J. Korean Math. Soc., 52-4 (2015) 699-725.
  • [4] Abdullayev F. G., Gün C.D., Ozkartepe N.P. Inequalities for algebraic polynomials in regions with exterior cusps. J. Nonlinear Funct. Anal., Article ID 3 (2015) 1-32.
  • [5] Abdullayev F.G., Özkartepe P. Uniform and pointwise polynomial inequalities in regions with cusps in the weighted Lebesgue space. Jaen Journal on Approximation, 7-2 (2015) 231-261.
  • [6] Abdullayev F.G., Özkartepe P., Polynomial inequalities in Lavrentiev regions with interior and exterior zero angles in the weighted Lebesgue space. Publications de l'Institut Mathématique (Beograd), 100-114 (2016) 209-227.
  • [7] Ahlfors L. Lectures on Quasiconformal Mappings. Princeton, NJ: Van Nostrand, 1966.
  • [8] Andrievskii V.V. On the uniform convergence of the Bieberbach polynomials in the regions with piecewise quasiconformal boundary, In: Theory of Mappings and approximation functions, "Naukovo Dumka", Kyiv, (1983) 3-18. (in Russian)
  • [9] Andrievskii V.V., Weighted Polynomial Inequalities in the Complex Plane. Journal of Approximation Theory, 164-9 (2012) 1165-1183.
  • [10] Andrievskii V.V., Belyi V.I. & Dzyadyk V.K. Conformal invariants in constructive theory of functions of complex plane. Atlanta:World Federation Publ.Com., 1995.
  • [11] Andrievskii V.V., Blatt H.P. Discrepancy of Signed Measures and Polynomial Approximation, Springer Verlag New York Inc., 2010.
  • [12] Dzjadyk V.K., Introduction to the Theory of Uniform Approximation of Function by Polynomials, Nauka, Moskow, 1977. (in Russian)
  • [13] Gaier D., On the convergence of the Bieberbach polynomials in regions with corners. Constructive Approximation, 4 (1988) 289-305.
  • [14] Jackson D., Certain problems on closest approximations. Bull. Amer. Math. Soc., 39 (1933) 889-906.
  • [15] Lehto O., Virtanen K.I., Quasiconformal Mapping in the plane, Springer Verlag, Berlin, 1973.
  • [16] Mamedhanov D.I., Inequalities of S.M.Nikol'skii type for polynomials in the complex variable on curves, Soviet Math.Dokl., 15 (1974) 34-37.
  • [17] Mamedhanov D.I., On Nikol'skii-type inequalities with new characteristics, Doklady Mathematics, 82 (2010) 882-883.
  • [18] Milovanovic G.V., Mitrinovic D.S. and Rassias Th.M., Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
  • [19] Nikol'skii S.M., Approximation of function of several variable and imbeding theorems, Springer-Verlag, New-York, 1975.
  • [20] Özkartepe N. P., Abdullayev F. G. , On the interference of the weight and boundary contour for algebraic polynomials in the weighted Lebesgue spaces I. Ukr. Math. J. 2016; 68(10): (Trans. from Ukr. Mat. Zh., 68-10 (2016) 1365-1379.
  • [21] Pritsker I.E., Comparing norms of polynomials in one and several variables, Journal of Math. Anal. and Appl., 216 (1997) 685-695.
  • [22] Pommerenke Ch., Univalent Functions, Göttingen, Vandenhoeck & Ruprecht, 1975.
  • [23] Rickman S., Characterization of quasiconformal arcs. Ann. Acad. Sci. Fenn., Ser. A, Mathematica, 395 (1966) 30 p.
  • [24] Stylianopoulos N., Strong asymptotics for Bergman polynomials over domains with corners and applications. Const. Approx., 38 (2013) 59-100.
  • [25] Suetin P.K., The ordinally comparison of various norms of polynomials in the complex domain, Matematicheskie zapiski Uralskogo Gos. Universiteta, 5-4 (1966) (in Russian).
  • [26] Suetin P. K., Main properties of the orthogonal polynomials along a circle, Uspekhi Math. Nauk, 21-2,128 (1966) 41-88.
  • [27] Suetin P.K., On some estimates of the orthogonal polynomials with singularities weight and contour. Sibirskiy Mat. Zhurnal, VIII-3 (1967) 1070-1078 (in Russian).
  • [28] Szegö G., Zygmund A., On certain mean values of polynomials. Journal d'Analyse Mathematique, 3-1 (1953) 225-244.
  • [29] Walsh J.L., Interpolation and Approximation by Rational Functions in the Complex Domain, AMS, 1960.

Uniform and Pointwise Polynomial Estimates in Regions with Interior and Exterior Cusps

Yıl 2018, Cilt: 39 Sayı: 1, 47 - 65, 16.03.2018

Pelin Özkartepe

https://doi.org/10.17776/csj.405512
Cited By: 4

Öz

In
this work, we investigate the estimation for algebraic polynomials in the
bounded and unbounded regions with piecewise Dini smooth curve having interior
and exterior zero angles.

Anahtar Kelimeler

Algebraic polynomials

Kaynakça

  • [1] Abdullayev F.G., Andrievskii V.V. On the orthogonal polynomials in the domains with -quasiconformal boundary. Izv. Akad. Nauk Azerb. SSR., Ser. FTM 1983; 1: 3-7.
  • [2] Abdullayev F. G., Özkartepe N. P., Gün C. D. Uniform and pointwise polynomial inequalities in regions without cusps in the weighted Lebesgue space. Bulletin of Tbilisi ICMC , 18-1 (2014) 146-167.
  • [3] Abdullayev F.G., Özkartepe P. On the growth of algebraic polynomials in the whole complex plane. J. Korean Math. Soc., 52-4 (2015) 699-725.
  • [4] Abdullayev F. G., Gün C.D., Ozkartepe N.P. Inequalities for algebraic polynomials in regions with exterior cusps. J. Nonlinear Funct. Anal., Article ID 3 (2015) 1-32.
  • [5] Abdullayev F.G., Özkartepe P. Uniform and pointwise polynomial inequalities in regions with cusps in the weighted Lebesgue space. Jaen Journal on Approximation, 7-2 (2015) 231-261.
  • [6] Abdullayev F.G., Özkartepe P., Polynomial inequalities in Lavrentiev regions with interior and exterior zero angles in the weighted Lebesgue space. Publications de l'Institut Mathématique (Beograd), 100-114 (2016) 209-227.
  • [7] Ahlfors L. Lectures on Quasiconformal Mappings. Princeton, NJ: Van Nostrand, 1966.
  • [8] Andrievskii V.V. On the uniform convergence of the Bieberbach polynomials in the regions with piecewise quasiconformal boundary, In: Theory of Mappings and approximation functions, "Naukovo Dumka", Kyiv, (1983) 3-18. (in Russian)
  • [9] Andrievskii V.V., Weighted Polynomial Inequalities in the Complex Plane. Journal of Approximation Theory, 164-9 (2012) 1165-1183.
  • [10] Andrievskii V.V., Belyi V.I. & Dzyadyk V.K. Conformal invariants in constructive theory of functions of complex plane. Atlanta:World Federation Publ.Com., 1995.
  • [11] Andrievskii V.V., Blatt H.P. Discrepancy of Signed Measures and Polynomial Approximation, Springer Verlag New York Inc., 2010.
  • [12] Dzjadyk V.K., Introduction to the Theory of Uniform Approximation of Function by Polynomials, Nauka, Moskow, 1977. (in Russian)
  • [13] Gaier D., On the convergence of the Bieberbach polynomials in regions with corners. Constructive Approximation, 4 (1988) 289-305.
  • [14] Jackson D., Certain problems on closest approximations. Bull. Amer. Math. Soc., 39 (1933) 889-906.
  • [15] Lehto O., Virtanen K.I., Quasiconformal Mapping in the plane, Springer Verlag, Berlin, 1973.
  • [16] Mamedhanov D.I., Inequalities of S.M.Nikol'skii type for polynomials in the complex variable on curves, Soviet Math.Dokl., 15 (1974) 34-37.
  • [17] Mamedhanov D.I., On Nikol'skii-type inequalities with new characteristics, Doklady Mathematics, 82 (2010) 882-883.
  • [18] Milovanovic G.V., Mitrinovic D.S. and Rassias Th.M., Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
  • [19] Nikol'skii S.M., Approximation of function of several variable and imbeding theorems, Springer-Verlag, New-York, 1975.
  • [20] Özkartepe N. P., Abdullayev F. G. , On the interference of the weight and boundary contour for algebraic polynomials in the weighted Lebesgue spaces I. Ukr. Math. J. 2016; 68(10): (Trans. from Ukr. Mat. Zh., 68-10 (2016) 1365-1379.
  • [21] Pritsker I.E., Comparing norms of polynomials in one and several variables, Journal of Math. Anal. and Appl., 216 (1997) 685-695.
  • [22] Pommerenke Ch., Univalent Functions, Göttingen, Vandenhoeck & Ruprecht, 1975.
  • [23] Rickman S., Characterization of quasiconformal arcs. Ann. Acad. Sci. Fenn., Ser. A, Mathematica, 395 (1966) 30 p.
  • [24] Stylianopoulos N., Strong asymptotics for Bergman polynomials over domains with corners and applications. Const. Approx., 38 (2013) 59-100.
  • [25] Suetin P.K., The ordinally comparison of various norms of polynomials in the complex domain, Matematicheskie zapiski Uralskogo Gos. Universiteta, 5-4 (1966) (in Russian).
  • [26] Suetin P. K., Main properties of the orthogonal polynomials along a circle, Uspekhi Math. Nauk, 21-2,128 (1966) 41-88.
  • [27] Suetin P.K., On some estimates of the orthogonal polynomials with singularities weight and contour. Sibirskiy Mat. Zhurnal, VIII-3 (1967) 1070-1078 (in Russian).
  • [28] Szegö G., Zygmund A., On certain mean values of polynomials. Journal d'Analyse Mathematique, 3-1 (1953) 225-244.
  • [29] Walsh J.L., Interpolation and Approximation by Rational Functions in the Complex Domain, AMS, 1960.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Natural Sciences
Yazarlar

Pelin Özkartepe

Yayımlanma Tarihi 16 Mart 2018
Gönderilme Tarihi 1 Ağustos 2017
Kabul Tarihi 6 Şubat 2018
Yayımlandığı Sayı Yıl 2018Cilt: 39 Sayı: 1

Kaynak Göster

APA Özkartepe, P. (2018). Uniform and Pointwise Polynomial Estimates in Regions with Interior and Exterior Cusps. Cumhuriyet Science Journal, 39(1), 47-65. https://doi.org/10.17776/csj.405512

Cited By

On the growth of the modulus of the derivative of algebraic polynomials in bounded and unbounded domains with cusps
Filomat
https://doi.org/10.2298/FIL2327243G
Inequalities of the Markov–Nikol’skii Type in Regions with Zero Interior Angles in the Bergman Space
Ukrainian Mathematical Journal
https://doi.org/10.1007/s11253-023-02208-4
Нерiвностi типу Маркова–Нiкольського в областях iз внутрiшнiми нульовими кутами в просторi Бергмана
Ukrains’kyi Matematychnyi Zhurnal
https://doi.org/10.37863/umzh.v75i3.7322
On the behaviour of derivative of algebraic polynomials in the regions with cusps
Applied Mathematics in Science and Engineering
https://doi.org/10.1080/27690911.2022.2076844
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