Inequalities Concerning Maximum Modulus of Higher Order Derivative of Complex Polynomials

Let P(z) be a complex polynomial of degree n. The problem of best approximation involving it’s derivative p’(z) under different restrictions on the zeros had been attracting many, including renowned scientists and mathematicians like Mandeleev, Markov brothers and Bernstein. Their works had been studied extensively by many mathematicians which resulted in rich collection of inequalities concerning complex polynomials. In this article, we discuss in brief, a summary of inequalities involving maximum modulus of higher order derivatives of complex polynomials