Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682215720240701Growth of the sth derivative of a polynomial with restricted zeros19804510.22075/ijnaa.2023.27169.3521ENReingachan NgamchuiDepartment of Mathematics, National Institute of Technology Manipur, Manipur-795004, IndiaKhangembam BabinaDeviDepartment of Mathematics, National Institute of Technology Manipur, Manipur-795004, IndiaBarchand ChanamDepartment of Mathematics, National Institute of Technology Manipur, Manipur-795004, IndiaJournal Article20220514In this paper, we establish some upper bound estimates for the maximum modulus of the higher order derivative of a polynomial with restricted zeros on a circle of $|z|=R$, $R\geq 1$, in terms of the maximum modulus of the same polynomial on the unit circle $|z|=1$. These results generalize and sharpen some known results in this direction.https://ijnaa.semnan.ac.ir/article_8045_ad7a9e7e1a42f0f17afbdb019d205e62.pdf