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

ABDULLAYEV, FAHREDDİN; Imashkyzy, M.

doi:10.2298/fil2510365a

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

ABDULLAYEV F., Imashkyzy M.

Filomat, cilt.39, sa.10, ss.3365-3379, 2025 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 39 Sayı: 10
Basım Tarihi: 2025
Doi Numarası: 10.2298/fil2510365a
Dergi Adı: Filomat
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
Sayfa Sayıları: ss.3365-3379
Anahtar Kelimeler: Algebraic polynomial, quasicircle, quasiconformal mapping
Uşak Üniversitesi Adresli: Evet

Özet

In this paper we study the growth of m − th derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces in bounded and unbounded regions of the complex plane, ignoring the recurrence formula. We also provide estimates in the whole complex plane.