Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve

P. Özkartepe

EN TR

Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve

Abstract

In this we continue studying the Nikolskii and Bernstein-Walsh type polynomial estimation in the Lebesgue spaces in the bounded and unbounded regions bounded by asymptotically conformal curve

Keywords

Polynomials, Nikolskii inequalities, Bernstein inequalities, Conformal mapping, Asymptotically conformal curve.

References

Abdullayev F.G., Andrievskii V.V., On the orthogonal polynomials in the domains with K -quasiconformal boundary. Izv. Akad. Nauk Azerb. SSR., Ser. FTM, 1, (1983), 3-7. [in Russian].
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.
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.
Abdullayev F.G., Özkartepe P., On the growth of algebraic polynomials in the wholecomplex plane, J. Korean Math. Soc. 52(4), (2015), 699-725.
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.
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.
Abdullayev F.G., Özkartepe N.P., Uniform and pointwise Bernstein-Walsh-type inequalities on a quasidisk in the complex plane, Bull. Belg. Math. Soc., 23 (2), (2016), 285-310.
Ahlfors L, Lectures on Quasiconformal Mappings. Princeton, NJ: Van Nostrand, (1966).
Anderson J. M., Becker J., Lesley F. D., Boundary values of asymptotically conformal mappings, J. London Math. Soc., 38, (1988), 453-462.
Andrievskii V.V., Constructive characterization of the harmonic functions in domains with quasiconformal boundary, In: Quasiconformal continuation and Approximation by function in the set of the complex plane. Kiev, (1985). [in Russian]

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).
Belinskii P.P., General Properties of Quasiconformal Mappings, Nauka, Sib. otd., Novosibirsk, (1974). [in Russian]
Becker J., Pommerenke C., Uber die quasikonforme Fortsetzung schlichten Funktionen, Math. Z., 161, (1978), 69-80.
Dzyadyk V.K., Shevchuk I.A., Theory of Uniform Approximation of Functions by Polynomials, Walter de Gruyter Berlin New York, (2008).
Dyn'kin E.M., Nonanalytic symmetry principle and conformal mappings. - St. Petersburg Math. J., 5, (1994), 523-544.
Gutlyanskii V., Ryazanov V., On asymptotically conformal curves, Complex Variables, 25, (1994), 357-366.
Gutlyanskii, V., Ryazanov V., On the local behaviour of quasi-conformal mappings, Izvestiya: Mathematics, 59 (3), (1995), 471-498.
Gutlyanskii V. Ya., Ryazanov V. I., On quasi-circles and asymptotically conformal circles, Dokl. Ross. Akad. Nauk, 330 (5), 546-548 (1993); (English transl., Russian Acad. Sci. Math., 47, (1993), 563-566.
Jackson D., Certain problems on closest approximations. Bull. Amer. Math. Soc., 39, (1933), 889-906.
Lehto O., Virtanen K.I., Quasiconformal Mapping in the plane, Springer Verlag, Berlin, (1973).
Lesley F.D., Hölder continuity of conformal mappings at the boundary via the strip method, Indiana Univ. Math. J., 31, (1982), 341-354.
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.
Mamedhanov D.I., On Nikolskii-type inequalities with new characteristics, Doklady Mathematics, 82, (2010), 882-883.
Milovanovic G.V., Mitrinovic D.S., Rassias Th.M., Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, (1994).
Nikol'skii S.M., Approximation of function of several variable and imbeding theorems, Springer-Verlag, New-York, (1975).
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., 68(10), (2016). (Trans. from Ukr. Mat. Zh., 68(10), (2016), 1365-1379).
Özkartepe P., Pointwise Bernstein-Walsh-type inequalities in regions with piecewise Dini-smooth boundary, MJEN, 5(3), (2017), 35-47.
Pommerenke Ch., Univalent Functions, Göttingen, Vandenhoeck & Ruprecht, (1975).
Pommerenke, Ch., Boundary Behaviour of Conformal Maps. - Springer-Verlag, Berlin, (1992).
Pommerenke Ch., Warschawski S.E., On the quantitative boundary behavior of conformal maps, Comment. Math. Helv., 57, (1982), 107-129.
Pritsker I., Comparing Norms of Polynomials in One and Several Variables, J. of Math. Anal. and Appl., 216, (1997), 685-695.
Stylianopoulos N., Strong asymptotics for Bergman polynomials over domains with corners and applications, Const. Approx., 33, (2013), 59-100.
Suetin P.K., The ordinally comparison of various norms of polynomials in the complex domain, Matematicheskie zapiski Uralskogo Gos. Universiteta, Vol.5 Tet. 4, (1966). [in Russian]
Suetin P. K., Main properties of the orthogonal polynomials along a circle, Uspekhi Math. Nauk 21(2(128)), (1966), 41-88.
Suetin P.K., On some estimates of the orthogonal polynomials with singularities weight and contour. Sibirskiy Mat. Zhurnal, Vol., VIII (3): (1967), 1070-1078. [in Russian]
Szegö G., Zygmund A., On certain mean values of polynomials. Journal d'Analyse Mathematique, 3(1), (1953), 225-244.
Walsh J.L., Interpolation and Approximation by Rational Functions in the Complex Domain, AMS, (1960).

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English

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Authors

P. Özkartepe This is me

Publication Date

May 1, 2018

Submission Date

May 1, 2018

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Year 2018 Volume: 6 Number: 1

IZ

https://izlik.org/JA45LM63NC

APA

Özkartepe, P. (2018). Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve. MANAS Journal of Engineering, 6(1), 26-45. https://izlik.org/JA45LM63NC

AMA

1.Özkartepe P. Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve. MJEN. 2018;6(1):26-45. https://izlik.org/JA45LM63NC

Chicago

Özkartepe, P. 2018. “Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve”. MANAS Journal of Engineering 6 (1): 26-45. https://izlik.org/JA45LM63NC.

EndNote

Özkartepe P (May 1, 2018) Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve. MANAS Journal of Engineering 6 1 26–45.

IEEE

[1]P. Özkartepe, “Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve”, MJEN, vol. 6, no. 1, pp. 26–45, May 2018, [Online]. Available: https://izlik.org/JA45LM63NC

ISNAD

Özkartepe, P. “Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve”. MANAS Journal of Engineering 6/1 (May 1, 2018): 26-45. https://izlik.org/JA45LM63NC.

JAMA

1.Özkartepe P. Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve. MJEN. 2018;6:26–45.

MLA

Özkartepe, P. “Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve”. MANAS Journal of Engineering, vol. 6, no. 1, May 2018, pp. 26-45, https://izlik.org/JA45LM63NC.

Vancouver

1.P. Özkartepe. Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve. MJEN [Internet]. 2018 May 1;6(1):26-45. Available from: https://izlik.org/JA45LM63NC

Manas Journal of Engineering

16155

Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve

Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve

Abstract

Keywords

Asimptotik konform eğri ile sınırlı bölgelerde düzgün ve noktasal polinom eşitsizlikleri

Abstract

Keywords

References

Details

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Published in Issue

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