On the maximum modulus of polynomials

Abstract

Abstract.The maximum modulus on \z\ = r < I of a polynomial of degree n not vanishing in \z\ < 1 is estimated in terms of its maximum modulus on \z\ = 1 and certain of its coefficients. Some other related problems are also considered.

A new inequality for a polynomial

“…Inequality (1.6) was also independently proved by Qazi [8,Lemma 1] who, in fact, has also proved the following result.…”

Some results concerning growth of polynomials

“…The following result which is an improvement as well as a generalization of a result due to Govil, Rahman and Schmeisser [13] (see also Qazi [18] ) follows from Corollary 3 by making R → 1.…”

Extensions of some polynomial inequalities to the polar derivative

“…(1.5) In the literature, there already exist some refinements and generalizations of all the above inequalities, for example see Chan and Malik [7], Qazi [16], Gardner, Govil and Weems [9], Govil [10] etc.…”