Research Article
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On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles

Year 2021, , 93 - 103, 30.06.2021
https://doi.org/10.51354/mjen.846484

Abstract

In this work we study Bernstein-Walsh-type estimations for the derivative of an arbitrary algebraic polynomial in regions with interior zero and exterior non zero angles.

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, 1983, 1, 3-7.
  • Abdullayev F. G., “On the interference of the weight boundary contour for orthogonal polynomials over the region”, J. of Comp. Anal. and Appl., 6 (1), 31-42, (2004).
  • Abdullayev F. G., Özkartepe P., “On the behavior of the algebraic polynomial in unbounded regions with piecewise dini-smooth boundary”, Ukr. Math. J. , Vol. 66 , No: 5, 2014, pp. 645-665.
  • Abdullayev F. G., Gün C. D., “On the behavior of the algebraic polynomials in regions with piecewise smooth boundary without cusps”, Ann. Polon. Math., 2014, 111, 39-58.
  • Abdullayev F. G., Gün C. D., Özkartepe P., “Inequalities for algebraic polynomials in regions with exterior cusps”, J. Nonlinear Funct. Anal. Article ID 3, 1-32, (2015).
  • Abdullayev F. G., Özkartepe P., “On the growth of algebraic polynomials in the whole complex plane”, J. Korean Math. Soc. 52(4, 699-725, (2015).
  • 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), 231-261, (2015).
  • 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), 209-227, (2016).
  • Abdullayev F. G., Aral D., “On the Bernstein-Walsh type Lemmas in regions of the complex plane”, Ukr. Math. J., Vol. 63 (3), 337-350, (2011).
  • Abdullayev F. G., Özkartepe P., “An analogue of the Bernstein-Walsh lemma in Jordan regions of the complex plane”, Journal Ineq. and Appl., 2013:570 7p, (2013).
  • Abdullayev F. G., Özkartepe P., “On the behavior of the algebraic polynomials in unbounded regions with piecewise dini-smooth boundary”, Ukr. Mat. J. – 2014. – 66 (5) – P. 575 – 597.
  • Abdullayev F. G., Özkartepe N.P., “Uniform and pointwise Bernstein-Walsh-type inequalities on a quasidisk in the complex plane”, Bull. Belg. Math. Soc., 2016, 23 (2), 285–310.
  • Abdullayev F. G., Gün C. D., “Bernstein-Walsh -type inequalities for derivatives of algebraic polynomials”, 2020. (to appear)
  • Ahlfors L., “Lectures on quasiconformal mappings”, Princeton, NJ: Van Nostrand, 1966.
  • Andrievskii V. V., “Weighted polynomial inequalities in the complex plane”, J. Approx.Theory, 2012, 164 (9), 1165-1183.
  • Andrievskii V. V., Belyi V. I., Dzyadyk V. K., “Conformal invariants in cocstructive theory of functions of complex plane”, Atlanta, World Federatin Publ. Com., 1995.
  • Belinskii P. P., “General properties of quasiconformal mappings”, Nauka, Sib. otd., Novosibirsk, 1974. [in Russian]
  • Dzyadyk V. K., “Introduction to the theory of uniform approximation of function by polynomials”, Nauka, Moskow, 1977.
  • Gaier D., “On the convergence of the Bieberbach polynomials in regions with corners”, Constructive Approximation, 4 (1988), pp.289-305.
  • Hille E., Szegö G., Tamarkin J. D., “On some generalization of a theorem of A.Markoff”, Duke Math., 3, 729-739, (1937).
  • Lehto O., Virtanen K.I., “Quasiconformal mapping in the plane”, Springer Verlag, Berlin, 1973.
  • Mergelyan S. N., “Some questions of constructive functions theory”, Proc. of the Steklov Institute of Mathematics, Vol. XXXVII, 1-92, 1951. [in Russian]
  • Özkartepe P., “Pointwise Bernstein-Walsh-type inequalities in regions with piecewise Dini-smooth boundary”, MJEN, 5(3), 35-47 (2017).
  • Rickman S., “Characterisation of quasiconformal arcs”, Ann. Acad. Sci. Fenn., Ser. A, Mathematica., 1966, 395 , 30 p.
  • Stylianopoulos N., “Strong asymptotics for Bergman polynomials over domains with corners and applications”, Const. Approx., 38, 59-100, (2013).
  • Tunc T., Şimşek D., Oruç E., “Pointwise Bernstein-Walsh-type inequalities in regions with interior zero angles in the Bergman space”, Trans. of NAS of Azerbaijan Ser. of Phys.-Tech. and Math. Sci.ences, vol. XXXVII, No 1, 1-12, 2017.
  • Walsh J. L., “Interpolation and approximation by rational functions in the complex domain”, AMS, 1960.
  • Warschawski S. E., “Über das Randverhalten der Ableitung der Abbildungsfunktion bei konformer Abbildung”, Math.Z., 35, 1932, pp.321-456.
Year 2021, , 93 - 103, 30.06.2021
https://doi.org/10.51354/mjen.846484

Abstract

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, 1983, 1, 3-7.
  • Abdullayev F. G., “On the interference of the weight boundary contour for orthogonal polynomials over the region”, J. of Comp. Anal. and Appl., 6 (1), 31-42, (2004).
  • Abdullayev F. G., Özkartepe P., “On the behavior of the algebraic polynomial in unbounded regions with piecewise dini-smooth boundary”, Ukr. Math. J. , Vol. 66 , No: 5, 2014, pp. 645-665.
  • Abdullayev F. G., Gün C. D., “On the behavior of the algebraic polynomials in regions with piecewise smooth boundary without cusps”, Ann. Polon. Math., 2014, 111, 39-58.
  • Abdullayev F. G., Gün C. D., Özkartepe P., “Inequalities for algebraic polynomials in regions with exterior cusps”, J. Nonlinear Funct. Anal. Article ID 3, 1-32, (2015).
  • Abdullayev F. G., Özkartepe P., “On the growth of algebraic polynomials in the whole complex plane”, J. Korean Math. Soc. 52(4, 699-725, (2015).
  • 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), 231-261, (2015).
  • 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), 209-227, (2016).
  • Abdullayev F. G., Aral D., “On the Bernstein-Walsh type Lemmas in regions of the complex plane”, Ukr. Math. J., Vol. 63 (3), 337-350, (2011).
  • Abdullayev F. G., Özkartepe P., “An analogue of the Bernstein-Walsh lemma in Jordan regions of the complex plane”, Journal Ineq. and Appl., 2013:570 7p, (2013).
  • Abdullayev F. G., Özkartepe P., “On the behavior of the algebraic polynomials in unbounded regions with piecewise dini-smooth boundary”, Ukr. Mat. J. – 2014. – 66 (5) – P. 575 – 597.
  • Abdullayev F. G., Özkartepe N.P., “Uniform and pointwise Bernstein-Walsh-type inequalities on a quasidisk in the complex plane”, Bull. Belg. Math. Soc., 2016, 23 (2), 285–310.
  • Abdullayev F. G., Gün C. D., “Bernstein-Walsh -type inequalities for derivatives of algebraic polynomials”, 2020. (to appear)
  • Ahlfors L., “Lectures on quasiconformal mappings”, Princeton, NJ: Van Nostrand, 1966.
  • Andrievskii V. V., “Weighted polynomial inequalities in the complex plane”, J. Approx.Theory, 2012, 164 (9), 1165-1183.
  • Andrievskii V. V., Belyi V. I., Dzyadyk V. K., “Conformal invariants in cocstructive theory of functions of complex plane”, Atlanta, World Federatin Publ. Com., 1995.
  • Belinskii P. P., “General properties of quasiconformal mappings”, Nauka, Sib. otd., Novosibirsk, 1974. [in Russian]
  • Dzyadyk V. K., “Introduction to the theory of uniform approximation of function by polynomials”, Nauka, Moskow, 1977.
  • Gaier D., “On the convergence of the Bieberbach polynomials in regions with corners”, Constructive Approximation, 4 (1988), pp.289-305.
  • Hille E., Szegö G., Tamarkin J. D., “On some generalization of a theorem of A.Markoff”, Duke Math., 3, 729-739, (1937).
  • Lehto O., Virtanen K.I., “Quasiconformal mapping in the plane”, Springer Verlag, Berlin, 1973.
  • Mergelyan S. N., “Some questions of constructive functions theory”, Proc. of the Steklov Institute of Mathematics, Vol. XXXVII, 1-92, 1951. [in Russian]
  • Özkartepe P., “Pointwise Bernstein-Walsh-type inequalities in regions with piecewise Dini-smooth boundary”, MJEN, 5(3), 35-47 (2017).
  • Rickman S., “Characterisation of quasiconformal arcs”, Ann. Acad. Sci. Fenn., Ser. A, Mathematica., 1966, 395 , 30 p.
  • Stylianopoulos N., “Strong asymptotics for Bergman polynomials over domains with corners and applications”, Const. Approx., 38, 59-100, (2013).
  • Tunc T., Şimşek D., Oruç E., “Pointwise Bernstein-Walsh-type inequalities in regions with interior zero angles in the Bergman space”, Trans. of NAS of Azerbaijan Ser. of Phys.-Tech. and Math. Sci.ences, vol. XXXVII, No 1, 1-12, 2017.
  • Walsh J. L., “Interpolation and approximation by rational functions in the complex domain”, AMS, 1960.
  • Warschawski S. E., “Über das Randverhalten der Ableitung der Abbildungsfunktion bei konformer Abbildung”, Math.Z., 35, 1932, pp.321-456.
There are 28 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Cevahir Doğanay Gün 0000-0003-3046-7667

Publication Date June 30, 2021
Published in Issue Year 2021

Cite

APA Gün, C. D. (2021). On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles. MANAS Journal of Engineering, 9(1), 93-103. https://doi.org/10.51354/mjen.846484
AMA Gün CD. On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles. MJEN. June 2021;9(1):93-103. doi:10.51354/mjen.846484
Chicago Gün, Cevahir Doğanay. “On Some Inequalities for Derivatives of Algebraic Polynomials in Unbounded Regions With Angles”. MANAS Journal of Engineering 9, no. 1 (June 2021): 93-103. https://doi.org/10.51354/mjen.846484.
EndNote Gün CD (June 1, 2021) On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles. MANAS Journal of Engineering 9 1 93–103.
IEEE C. D. Gün, “On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles”, MJEN, vol. 9, no. 1, pp. 93–103, 2021, doi: 10.51354/mjen.846484.
ISNAD Gün, Cevahir Doğanay. “On Some Inequalities for Derivatives of Algebraic Polynomials in Unbounded Regions With Angles”. MANAS Journal of Engineering 9/1 (June 2021), 93-103. https://doi.org/10.51354/mjen.846484.
JAMA Gün CD. On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles. MJEN. 2021;9:93–103.
MLA Gün, Cevahir Doğanay. “On Some Inequalities for Derivatives of Algebraic Polynomials in Unbounded Regions With Angles”. MANAS Journal of Engineering, vol. 9, no. 1, 2021, pp. 93-103, doi:10.51354/mjen.846484.
Vancouver Gün CD. On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles. MJEN. 2021;9(1):93-103.

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