If we restrict ourselves to the class of polynomials having no zeros in |z| then inequality （ ） can be sharpened. In fact it was shown by Ankeny and Rivlin， - that if p（z） in |z| then （ ） can be replaced by
　　By involving the coefficients of p（z） Dewan and Ahuja ， - in the same paper obtained the following refinement of Theorem A.
　　Theorem B.. If （ ） ∑is a polynomial of degree n having all its zeros on| | ？ ？ then for every positive integer s*？（ ？）+？
　　In this paper we restrict ourselves to the class of polynomials of degree n having all its zeros on |z| k k and obtain an improvement and generalization of Theorem A and Theorem B. More precisely we prove Theorem .. If （ ） ∑is a polynomial of degree n having all its zeros on| | ？ ？ then for every positive integer s and R
　　For the proof of these theorems we need the following lemmas. Lemma .. If （ ） ∑？？ ？ ？ is a polynomial of degree having all its zeros on| | ？ ？ then
　　From which we get the desired result.
　　The proof of inequality （ ） follows on the same lines as that of inequality （9） but instead of using inequality （ 5） of Lemma 3 we use inequality （ 6） of Lemma 3.
　　 REFERENCES
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