A comparison inequality for rational functions
Author:
Xin Li
Journal:
Proc. Amer. Math. Soc. 139 (2011), 16591665
MSC (2010):
Primary 26D10, 26Cxx; Secondary 30A10, 30C15
Published electronically:
September 16, 2010
MathSciNet review:
2763755
Fulltext PDF
Abstract 
References 
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Additional Information
Abstract: We establish a new inequality for rational functions and show that it implies many inequalities for polynomials and their polar derivatives.
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 A. Aziz, Inequalities for the polar derivative of a polynomial, J. Approx. Theory, 55 (1988), 183193. MR 965215 (89m:30010)
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 A. Aziz and W.M. Shah, Inequalities for the polar derivative of a polynomial, Indian J. Pure Appl. Math., 29 (1998), 163173. MR 1623254 (2000b:30002)
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 P. Borwein and T. Erdélyi, Sharp extensions of Bernstein inequalities to rational spaces, Mathematika, 43 (1996), 413423. MR 1433285 (97k:26014)
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 F.F. Bonsall and M. Marden, Critical points of rational functions with selfinversive polynomial factors, Proc. Amer. Soc., 5 (1954), 111114. MR 0060016 (15:613a)
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 M.A. Malik and M.C. Vong, Inequalities concerning the derivative of polynomials, Rendiconts Del Circolo Matematico Di Palermo Serie II, 34 (1985), 422426. MR 848119 (88c:41026)
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 M. Marden, Geometry of Polynomials, Math. Surveys, No. 3, Amer. Math. Soc., Providence, Rhode Island, 1966. MR 0225972 (37:1562)
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 R.N. Mohapatra and W.M. Shah, Inequalities for the polar derivative of a polynomial, preprint, 2008.
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 Q.I. Rahman and G. Schmeisser, Analytic theory of polynomials, Oxford University Press, Oxford, 2002. MR 1954841 (2004b:30015)
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 V.I. Smirnov and N.A. Lebedev, Function of a Complex Variable, English edition, Iliffe Books, Landon, 1968.
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Additional Information
Xin Li
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email:
xli@math.ucf.edu
DOI:
http://dx.doi.org/10.1090/S00029939201010624X
Keywords:
Bernstein inequality,
rational functions,
polar derivative
Received by editor(s):
February 4, 2010
Received by editor(s) in revised form:
May 17, 2010
Published electronically:
September 16, 2010
Communicated by:
Walter Van Assche
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
