Results for self-Inversive rational functions
DOI :
https://doi.org/10.5269/bspm.65843Résumé
In this paper, we find some relations between maximum modulus of a rational function r(z) satisfying r(z) = B(z)r(1/z) and the maximum modulus of its derivative. We also find analogue of Chon’s Theorem for rational functions.
Références
[1] A. Aziz, Inequalities for the polar derivative of polynomial, J. Approx. Theory, 55 (1988), 183-193.
[2] A. Aziz and W. M. Shah, Inequalities for the polar derivative of a polynomial, Indian J. Pure Appl. Math., 29(2) (1998), 163-173.
[3] S. N. Bernstein, Sur e'ordre de la meilleure approximation des functions continues par des polynomes de degre' donne', Mem. Acad. R. Belg., 4 (1912), 1-103.
[4] A. Cohn, Uber die Anzahl der wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z. 14(1922): 110-148
[5] M. A. Malik, On the derivative of a polynomial, J. Lond. Math. Soc. 1 (1969), 57-60.
[6] Xin Li, R. N. Mohapatra and R. S. Rodgriguez, Bernstein inequalities for rational functions with prescribed poles, J. London Math. Soc., 51 (1995), 523-531.
[7] W. M. Shah and A. Liman, On some Bernstein type inequalities for polynomials, Nonlinear Funct. Anal. Appl,, 2 (2004), 223-232.
[8] W.M. Shah, A Generalization of a Theorem of Paul Turan, Journal of Ramanujan Society, 1(1996), 29-35.
[2] A. Aziz and W. M. Shah, Inequalities for the polar derivative of a polynomial, Indian J. Pure Appl. Math., 29(2) (1998), 163-173.
[3] S. N. Bernstein, Sur e'ordre de la meilleure approximation des functions continues par des polynomes de degre' donne', Mem. Acad. R. Belg., 4 (1912), 1-103.
[4] A. Cohn, Uber die Anzahl der wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z. 14(1922): 110-148
[5] M. A. Malik, On the derivative of a polynomial, J. Lond. Math. Soc. 1 (1969), 57-60.
[6] Xin Li, R. N. Mohapatra and R. S. Rodgriguez, Bernstein inequalities for rational functions with prescribed poles, J. London Math. Soc., 51 (1995), 523-531.
[7] W. M. Shah and A. Liman, On some Bernstein type inequalities for polynomials, Nonlinear Funct. Anal. Appl,, 2 (2004), 223-232.
[8] W.M. Shah, A Generalization of a Theorem of Paul Turan, Journal of Ramanujan Society, 1(1996), 29-35.
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Publié
2024-05-08
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Research Articles
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