Integral norm estimates for the polar derivative of Lacunary-type complex polynomials

Abdullah Mir
2020 Applicable Analysis and Discrete Mathematics  
In this paper, we prove some integral-norm inequalities for the polar derivative of Lacunary-type complex polynomials having zeros in closed exterior or closed interior of a circle. The results obtained besides derive polar derivative analogues of some classical Bernstein and Tur?n-type inequalities for the uniform-norm also include several interesting generalizations and refinements of some integral-norm inequalities for polynomials as well.
doi:10.2298/aadm200412036m fatcat:j4oetd76dreptkzdztem7oe4zu