Document Type : Research Paper

Authors

• Shabir Ahmad Malik ¹
• Bashir Ahmad Zargar ²
• F.A. Zargar ²
• F.A. Sofi ³

¹ Department of Mathematics, University of Kashmir , Srinagar, Jammu and Kashmir, India

² Department of Mathematics, University of Kashmir, Srinagar, Jammu and Kashmir, India

³ Department of Mathematics, Govt. College for Women, M.A. Road, Srinagar - 190001, Jammu and Kashmir, India

Abstract

In this paper some sharp lower bound estimates for the maximal modulus of $p'(z)$ and polar derivative of $p(z)$ are established in terms of their degrees, coefficients and maximal modulus of $p(z)$ over unit disk under the assumption that all the zeros of $p(z)$ lie in $|z|\leq k$, $k \geq 1$.

Keywords

• Lower bound
• Maximum modulus
• Polar derivative
• Polynomial