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Abstract: For a polynomial p(z) of degree n, having no zeros in
|z| < 1 Ankeny and Rivlin had shown that for R ≥ 1
max
|z|=R|p(z)| ≤Rn+ 1
2 max
|z|=1|p(z)|.
Using Govil, Rahman and Schmeisser’s refinement of the generalization of Schwarz’s lemma we have obtained a refinement of Ankeny and Rivlin’s result. Our refinement is also a refinement of Dewan and Pukhta’s refine- ment of Ankeny and Rivlin’s result.
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