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2023 | OriginalPaper | Chapter

Growth of Polynomials Having No Zero Inside a Circle

Authors : Khangembam Babina Devi, N Reingachan, Thangjam Birkramjit Singh, Barchand Chanam

Published in: Frontiers in Industrial and Applied Mathematics

Publisher: Springer Nature Singapore

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Abstract

The chapter delves into the growth of polynomials with no zeros inside a specified circle, building upon the Maximum Modulus Principle and previous works by Ankeny, Rivlin, and Govil. It presents a refined and generalized inequality, Theorem 1, which improves upon Hussain's result and has significant implications for understanding polynomial behavior. The manuscript also discusses various corollaries and lemmas, showcasing the monotonicity of certain functions and providing exact values for specific cases. Through these explorations, the chapter offers a comprehensive analysis of the subject, making it a valuable resource for specialists in the field.

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Title: Growth of Polynomials Having No Zero Inside a Circle
Authors: Khangembam Babina Devi
N Reingachan
Thangjam Birkramjit Singh
Barchand Chanam
Publisher: Springer Nature Singapore
Book: Frontiers in Industrial and Applied Mathematics
Print ISBN: 978-981-19-7271-3

Electronic ISBN: 978-981-19-7272-0

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-981-19-7272-0_32

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