On an inequality of S. Bernstein and estimates for the moduli of the zeros of a polynomial.

The present thesis entitled “On an inequality of S. Bernstein and estimates for the moduli of the zeros of a polynomial" is an outcome of the work carried out by author during the last two years at the Post Graduate Department of Mathematics, University of Kashmir, Srinagar. This Thesis consists of four chapters. In the first chapter, we have studied inequalities on the Maximum Modulus of a Polynomial and its Derivative. In the second chapter, we considered Lacunary type polynomials and obtain inequalities concerning the polar derivative of a polynomial. The third chapter deals with certain problems concerning a family of B operators preserving the inequalities between polynomials. Fourth chapter concerns with the location of the zeros of a polynomial with restricted coefficients.Digital copy of Ph.D thesis.University of Kashmir