On the Erdos Lax Inequalities and Bounds for Zeros of Polynomials with Restricted Coefficients

Abstract

The present thesis entitled quotOn the Erdös-Lax type inequalities and bounds for zeros of polynomials with restricted coefficientsquot is an outcome of the work carried out by the author during the last three years at the Post Graduate Department of Mathematics, University of Kashmir, Srinagar. This thesis consists of the following four chapters. newlineIn Chapter I, we present some definitions and relevant results which are required in subsequent sections. newlineIn Chapter II, we have obtained refinements and generalizations of some recent results due to Aziz, Breaz, Milovanoviand#263;, Mir and others. Here, we have extended some well-known inequalities involving the polar derivative of a polynomial with s-fold zeros at the origin. newlineIn chapter III, the estimates obtained strength some familiar rational inequalities of Mir, Hans, Aziz and Zargar. Additionally, the obtained results extend some recent results of Dubinin. newlineIn chapter IV, we have generalized various results of Eneström-Kakeya type from the complex to quaternionic setting. newline newline