On the behavior of the modulus of $m$-th derivatives of the algebraic polynomials in the whole complex plane without recurrence formula in the weighted Bergman space

Authors

  • F. G. Abdullayev Usak University, Faculty of Engineering and Natural Sciences, Usak, Turkiye; Institute of Mathematics and Mechanics MSE Republic of Azerbaijan, Baku, Azerbaijan
  • M. Imashkyzy Kyrgyz-Turkish Manas University, Bishkek, Kyrgyz Republic

DOI:

https://doi.org/10.3842/umzh.v78i1-2.8778

Keywords:

Bernstein-Markoff inequality, Walsh inequality, Algebraic polynomial, Quasiconformal mapping, Quasicircle,

Abstract

UDC 517.5

We study the problem of growth of the $m$th derivatives of an arbitrary algebraic polynomial in weighted Bergman spaces in unbounded domains of the complex plane, without using the recurrence relation. We consider $k$-quasidisks and quasidisks with some additional functional conditions. These conditions enable us to combine several known classes of curves into a single class and obtain estimates for the growth of $m$th derivatives in this common class. By using similar estimates obtained for bounded quasidisks, we also provide estimates valid in the whole complex plane.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 1-2, 2026.

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Published

26.01.2026

Issue

Vol. 78 No. 1-2 (2026)

Section

Research articles

License

Copyright (c) 2026 F. G. Abdullayev, M. Imashkyzy

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Abdullayev, F. G., and M. Imashkyzy. “On the Behavior of the Modulus of $m$-Th Derivatives of the Algebraic Polynomials in the Whole Complex Plane Without Recurrence Formula in the Weighted Bergman Space”. Ukrains’kyi Matematychnyi Zhurnal, vol. 78, no. 1-2, Jan. 2026, pp. 71–72, https://doi.org/10.3842/umzh.v78i1-2.8778.