On Sharpening of a Theorem of Ankeny and Rivlin
Year: 2020
Author: Aseem Dalal, N. K. Govil
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 2 : pp. 225–234
Abstract
Let p(z)=∑nv=0avzv be a polynomial of degree n,
M(p,R)=:max|z|=R≥0|p(z)| and M(p,1)=:||p||.
Then according to a well-known result of Ankeny and Rivlin [1], we have for R≥1, M(p,R)≤(Rn+12)||p||.This inequality has been sharpened by Govil [4], who proved that for R≥1, M(p,R)≤(Rn+12)||p||−n2(||p||2−4|an|2||p||){(R−1||p||)||p||+2|an|−ln(1+(R−1)||p||||p||+2|an|)}.In this paper, we sharpen the above inequality of Govil [4], which in turn sharpens the
inequality of Ankeny and Rivlin [1].
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2018-0001
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 2 : pp. 225–234
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Inequalities polynomials zeros.
Author Details
Aseem Dalal Email
N. K. Govil Email
-
Frontiers in Industrial and Applied Mathematics
Growth of Polynomials Having No Zero Inside a Circle
Devi, Khangembam Babina | Reingachan, N | Singh, Thangjam Birkramjit | Chanam, Barchand2023
https://doi.org/10.1007/978-981-19-7272-0_32 [Citations: 0] -
Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomial
Different types of Bernstein inequalities
Gardner, Robert B. | Govil, Narendra K. | Milovanović, Gradimir V. | Rassias, Themistocles M.2022
https://doi.org/10.1016/B978-0-12-811988-4.00009-8 [Citations: 0] -
Growth of polynomials not vanishing inside a circle
Devi, Khangembam Babina | Singh, Thangjam Birkramjit | Soraisam, Robinson | Chanam, BarchandThe Journal of Analysis, Vol. 30 (2022), Iss. 4 P.1439
https://doi.org/10.1007/s41478-022-00410-4 [Citations: 0] -
A note on sharpening of a theorem of Ankeny and Rivlin
Dalal, Aseem | Govil, N.K.Applicable Analysis and Discrete Mathematics, Vol. 17 (2023), Iss. 1 P.273
https://doi.org/10.2298/AADM200206012D [Citations: 2] -
Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomial
Bibliography
2022
https://doi.org/10.1016/B978-0-12-811988-4.00014-1 [Citations: 0]