Operators and Growth of Polynomials

Abstract

The present thesis entitled quotOperators and growth of polynomialsquot is an outcome of the work carried out by author during the last three years at the Post Graduate Department of Mathematics, University of Kashmir, Srinagar.This thesis consists of four chapters. The first chapter contains introduction and statements of results.In chapter II, we have obtained refiements and generalizations of some results due to Jain [57], Govil, Qazi and Rahman [47] and others. We also obtain some Turan type inequalities for the sth derivative of a polynomial having a zero of order t at the origin.In chapter III, we have obtained a bound which is a better than the bound obtained recently by Dubinin [38]. Our results also strengthen the results of Aziz and Dawood [8] and Ankeny and Rivlin [1]. We also proved the extensions of results due to Govil and Nwaeze [52].In chapter IV, we extend some results to the polar derivative of a polynomial and thereby obtain the generalizations of the results due to Shah [97],Dubinin [38] and Aziz and Rather [12]. We also proved some Lp mean extensions of certain well known polynomial inequalities, which in particular generalizes and renes the results due to Rather, Gulzar and Ahangar [89],Aziz and Rather [12] and Mir and Baba [71] and others.