Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary

Cevahir Doğanay Gün

doi:10.17776/csj.1723278

Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary

Abstract

In this paper, we investigate inequalities for higher order derivatives of algebraic polynomials in weighted Lebesgue space. In doing so, using the weighted L_p-norm, we establish the growth of the modulus of the m-th derivatives of algebraic polynomials on the closure and outside of a given region of the complex plane bounded by a piecewise smooth curve with interior zero angles. As a result, we estimate the growth rate of the derivatives of algebraic polynomials on the whole complex plane depending on the parameters of the region under consideration.

Keywords

Bernstein inequality, polynomial estimates, quasiconformal curve, piecewise smooth curve

References

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Cevahir Doğanay Gün ^*
0000-0003-3046-7667
Türkiye

Publication Date

September 30, 2025

Submission Date

June 19, 2025

Acceptance Date

August 20, 2025

Published in Issue

Year 2025 Volume: 46 Number: 3

DOI

https://doi.org/10.17776/csj.1723278

IZ

https://izlik.org/JA93EY23YG

APA

Gün, C. D. (2025). Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary. Cumhuriyet Science Journal, 46(3), 572-582. https://doi.org/10.17776/csj.1723278

AMA

1.Gün CD. Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary. CSJ. 2025;46(3):572-582. doi:10.17776/csj.1723278

Chicago

Gün, Cevahir Doğanay. 2025. “Some Estimates of the Growth of Polynomials in the Region With Piecewise Smooth Boundary”. Cumhuriyet Science Journal 46 (3): 572-82. https://doi.org/10.17776/csj.1723278.

EndNote

Gün CD (September 1, 2025) Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary. Cumhuriyet Science Journal 46 3 572–582.

IEEE

[1]C. D. Gün, “Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary”, CSJ, vol. 46, no. 3, pp. 572–582, Sept. 2025, doi: 10.17776/csj.1723278.

ISNAD

Gün, Cevahir Doğanay. “Some Estimates of the Growth of Polynomials in the Region With Piecewise Smooth Boundary”. Cumhuriyet Science Journal 46/3 (September 1, 2025): 572-582. https://doi.org/10.17776/csj.1723278.

JAMA

1.Gün CD. Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary. CSJ. 2025;46:572–582.

MLA

Gün, Cevahir Doğanay. “Some Estimates of the Growth of Polynomials in the Region With Piecewise Smooth Boundary”. Cumhuriyet Science Journal, vol. 46, no. 3, Sept. 2025, pp. 572-8, doi:10.17776/csj.1723278.

Vancouver

1.Cevahir Doğanay Gün. Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary. CSJ. 2025 Sep. 1;46(3):572-8. doi:10.17776/csj.1723278

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Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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