On integral extension of Ankeny and Rivlin-type inequality

Nirmal Kumar Singha, Barchand Chanam

Abstract


A well-known theorem due to Ankeny and Rivlin states that if p(z) is a polynomial of degree n having no zero in |z| < 1, then
max        |p(z)| <= (Rn+1)/2  max   |p(z)|. 
|z|=R>=1                            |z|=1
In this paper, we obtain an extension as well as an improvement of this inequality to the integral setting.


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References


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DOI: https://doi.org/10.52846/ami.v52i2.2017