Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A comparison inequality for rational functions


Author: Xin Li
Journal: Proc. Amer. Math. Soc. 139 (2011), 1659-1665
MSC (2010): Primary 26D10, 26Cxx; Secondary 30A10, 30C15
DOI: https://doi.org/10.1090/S0002-9939-2010-10624-X
Published electronically: September 16, 2010
MathSciNet review: 2763755
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We establish a new inequality for rational functions and show that it implies many inequalities for polynomials and their polar derivatives.


References [Enhancements On Off] (What's this?)

  • 1. A. Aziz, Inequalities for the polar derivative of a polynomial, J. Approx. Theory, 55 (1988), 183-193. MR 965215 (89m:30010)
  • 2. A. Aziz and W.M. Shah, Inequalities for the polar derivative of a polynomial, Indian J. Pure Appl. Math., 29 (1998), 163-173. MR 1623254 (2000b:30002)
  • 3. P. Borwein and T. Erdélyi, Polynomial Inequalities, Springer-Verlag, New York, 1995. MR 1367960 (97e:41001)
  • 4. P. Borwein and T. Erdélyi, Sharp extensions of Bernstein inequalities to rational spaces, Mathematika, 43 (1996), 413-423. MR 1433285 (97k:26014)
  • 5. F.F. Bonsall and M. Marden, Critical points of rational functions with self-inversive polynomial factors, Proc. Amer. Soc., 5 (1954), 111-114. MR 0060016 (15:613a)
  • 6. N.K. Govil, On the derivative of a polynomial, Proc. Amer. Math. Soc., 41 (1973), 543-546. MR 0325932 (48:4278)
  • 7. N.K. Govil, G. Nyuydinkong, and B. Tameru, Some $ L^p$ inequalities for the polar derivative of a polynomial, J. Math. Anal. Appl., 254 (2001), 618-626. MR 1805528 (2001m:41007)
  • 8. P.D. Lax, Proof of a conjecture of P. Erdös on the derivative of a polynomial, Bull. Amer. Math. Soc., 50 (1944), 509-513. MR 0010731 (6:61f)
  • 9. X. Li, R.N. Mohapatra, and R.S. Rodgriguez, Bernstein-type inequalities for rational functions with prescribed poles, J. London Math. Soc., 51 (1995), 523-531. MR 1332889 (96b:30005)
  • 10. M.A. Malik and M.C. Vong, Inequalities concerning the derivative of polynomials, Rendiconts Del Circolo Matematico Di Palermo Serie II, 34 (1985), 422-426. MR 848119 (88c:41026)
  • 11. M. Marden, Geometry of Polynomials, Math. Surveys, No. 3, Amer. Math. Soc., Providence, Rhode Island, 1966. MR 0225972 (37:1562)
  • 12. R.N. Mohapatra and W.M. Shah, Inequalities for the polar derivative of a polynomial, preprint, 2008.
  • 13. Q.I. Rahman and G. Schmeisser, Analytic theory of polynomials, Oxford University Press, Oxford, 2002. MR 1954841 (2004b:30015)
  • 14. V.I. Smirnov and N.A. Lebedev, Function of a Complex Variable, English edition, Iliffe Books, Landon, 1968.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 26D10, 26Cxx, 30A10, 30C15

Retrieve articles in all journals with MSC (2010): 26D10, 26Cxx, 30A10, 30C15


Additional Information

Xin Li
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: xli@math.ucf.edu

DOI: https://doi.org/10.1090/S0002-9939-2010-10624-X
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.

American Mathematical Society