A Note on Tur\(\acute{a}\)n-Type Inequalities for Polynomials

Abstract

For a polynomial p(z) over the field of complex numbers, finding lower bound of |\(P^{\prime}\)(z)| in term of |p(z)| with restriction on zeros of the polynomial also known as Tur\(\acute{a}\)n-type inequalities is a classical topic in analysis. In this article, we investigate and analyse certain factors which improve the bound on such inequalities namely zeros and coecient of the polynomial.