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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제32권 제3호
- 발행연도
- 2014.1
- 수록면
- 297 - 302 (6page)
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A well known result due to Ankeny and Rivlin [1] states that if $p(z)={\sum}^n_{j=0}a_jz^j$ is a polynomial of degree n satisfying $p(z){\neq}0$ for |z| < 1, then for $R{\geq}1$ $$\max_{{\mid}z{\mid}=R}{\mid}p(z){\mid}{\leq}{\frac{R^n+1}{2}}\max_{{\mid}z{\mid}=1}{\mid}p(z){\mid}$$. It was proposed by Professor R.P. Boas Jr. to obtain an inequality analogous to this inequality for polynomials having no zeros in |z| < k, k > 0. In this paper, we obtain some results in this direction, by considering polynomials of degree $n{\geq}2$, having all its zeros on the disk |z| = k, $k{\leq}1$.
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참고문헌 (6)
참고문헌 신청
N.C. Ankeny / 1955 / Rivlin,On a Theorem of S. Bernstein / Pacifc J. Math 5:849~852
K.K. Dewan / 2011 / Growth of polynomials with prescribed zeros / J. Math. Inequalities 5(3):355~361
K.K. Dewan / 2007 / Note on a Theorem of S. Bernstein / Southeast Asian Bulletin of Math 31:691~695
C. Frappier / 1985 / New inequalities for polynomials / Trans. Amer. Math. Soc 288:69~99
N.K. Govil / 1980 / On the Theorem of S. Bernstein / J. Math. and Phy. Sci 14:183~187
K.K. Dewan / 2011 / Growth of polynomials with prescribed zeros / J. Math. Inequalities 5(3):355~361
K.K. Dewan / 2007 / Note on a Theorem of S. Bernstein / Southeast Asian Bulletin of Math 31:691~695
C. Frappier / 1985 / New inequalities for polynomials / Trans. Amer. Math. Soc 288:69~99
N.K. Govil / 1980 / On the Theorem of S. Bernstein / J. Math. and Phy. Sci 14:183~187
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