On Bernstein-Type Inequalities for Rational Functions with Prescribed Poles

In this paper, we shall use a parameter β and obtain some Bernstein-type inequalities for rational functions with prescribed poles which generalize the results of Qasim and Liman and Li, Mohapatra and Rodriguez and others.

Bernstein Type Inequalities for Polar Derivative of Polynomial

If is a polynomial of degree n such that in , , then Govil [ Proc. Nat. Acad. Sci., Vol. 50, pp. 50-52, 1980. ] proved provided and attain their maxima at the same point on the circle , where . Equality in the above inequality holds for. In this paper, we extend the above inequality and an improved version of this into polar derivative of a polynomial.