On bifurcation points of a complex polynomial

On Bernstein Type Inequalities for Complex Polynomial

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

The Density of Extreme Points in Complex Polynomial Approximation

Let K be a compact set in the complex plane having connected and regular complement, and let / be any function continuous on K and analytic in the interior of K. For the polynomials pn(¡) of respective degrees at most n of best uniform approximation to / on K, we investigate the density of the sets of extreme points And) :={zeK: \f{z) p*n{f)(z)\ = \\f Pn(¡)\\K} in the boundary of K.

Polynomial Points

We determine the infinite sequences (ak) of integers that can be generated by polynomials with integral coefficients, in the sense that for each finite initial segment of length n there is an integral polynomial fn(x) of degree < n such that ak = fn(k) for k = 0, 1, . . . , n − 1. Let P be the set of such sequences and Π the additive group of all infinite sequences of integers. Then P is a subg...

On the polar derivative of a polynomial

For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...

On Szeged Polynomial of a Graph