#### Title

Inequalities for polynomials not vanishing in a disk

#### 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

#### ISSN

0096-3003

#### Recommended Citation

"Inequalities for polynomials not vanishing in a disk" (2011). *Faculty Bibliography 2010s*. 1561.

http://stars.library.ucf.edu/facultybib2010/1561

## Comments

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