Inequalities for polynomials not vanishing in a disk

    Authors

    A. Liman; R. N. Mohapatra;W. M. Shah

    Comments

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    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    Polynomials; Zeros; Inequalities in the complex domain; BERNSTEIN; Mathematics, Applied

    Abstract

    If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all alpha, beta is an element of C with vertical bar alpha vertical bar <= 1, vertical bar beta vertical bar < = 1, it is known that. vertical bar P(Rz) - alpha P(z) + beta{(R+1/2)(n) - vertical bar alpha vertical bar}P(z)vertical bar < = 1/2[vertical bar R(n) - alpha + beta{(R + 1/2)(n) - vertical bar alpha vertical bar}vertical bar vertical bar Z vertical bar(n) + vertical bar 1 - alpha + beta{(R + 1/2)(n) - vertical bar alpha vertical bar}vertical bar] max(vertical bar z vertical bar=1) vertical bar P(z)vertical bar, for R > = 1 and vertical bar z vertical bar > = 1. The present paper contains a generalization and an improvement of this and some other polynomial inequalities of similar nature. (C) 2011 Elsevier Inc. All rights reserved.

    Journal Title

    Applied Mathematics and Computation

    Volume

    218

    Issue/Number

    3

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    949

    Last Page

    955

    WOS Identifier

    WOS:000294298400056

    ISSN

    0096-3003

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