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On the Erdös–Lax-Type Inequalities for Polynomials.

Authors :
Nazir, I.
Wani, I. A.
Source :
Journal of Contemporary Mathematical Analysis; Aug2024, Vol. 59 Issue 4, p290-294, 5p
Publication Year :
2024

Abstract

Erdös–Lax inequality relates the sup norm of the derivative of a polynomial along the unit circle to that of the polynomial itself (on the unit circle). This paper aims to extend the classical Erdös–Lax inequality to the polar derivative of a polynomial by using the extreme coefficients of the given polynomial. The obtained results not only enrich the realm of Erdös–Lax-type inequalities but also offer a promising avenue for diverse applications where these inequalities play a pivotal role. To illustrate the practical significance of our results, we present a numerical example. It vividly demonstrates that our bounds are considerably sharper than the existing ones in the extensive literature on this captivating subject. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10683623
Volume :
59
Issue :
4
Database :
Complementary Index
Journal :
Journal of Contemporary Mathematical Analysis
Publication Type :
Academic Journal
Accession number :
178953047
Full Text :
https://doi.org/10.3103/S1068362324700195