Inequalities of Turán Type for the Polar Derivative of a Polynomial.

This paper mainly studies the well-known Turán type inequalities that relate the uniform norm of a polynomial to its derivative on the unit disk in the plane. We derive some new inequalities that relate the uniform norm of the polar derivative to the underlying polynomial when the zeros are within a closed disk. The obtained results produce various inequalities that are sharper than those available in a very rich literature on the subject. [ABSTRACT FROM AUTHOR]