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 circle where .
 Equality above inequality holds for.
 In this paper, we extend an improved version into polar derivative polynomial.

It is well-known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial pn(x) interlace with the zeros of pn(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of k-th, 1 ≤ k ≤ n − 1, zeros of the associated polynomial and the derivative of an orthogonal...

We introduce a “workable” notion of degree for non-homogeneous polynomial ideals and formulate prove ideal theoretic Bézout inequalities the sum two in terms this generators.

Different types of polynomial inequalities have been studied since more one century. The first type is the so-called Markov-Bernstein inequalities (A. A. Markov in 1889 [5]). More recently other inequalities involving the Lnorm for the Hermite measure were given (see Bojanov and Varma [2], Alves and Dimitrov [1]). Inequalities given in the previous papers are particular cases of the more genera...

Throughout his life Erdős showed a particular fascination with inequalities for constrained polynomials. One of his favorite type of polynomial inequalities was Markovand Bernstein-type inequalities. For Erdős, Markovand Bernstein-type inequalities had their own intrinsic interest. He liked to see what happened when the polynomials are restricted in certain ways. Markovand Bernstein-type inequa...