Results for self-Inversive rational functions
Abstract
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.
Downloads
References
A. Aziz, Inequalities for the polar derivative of polynomial, J. Approx. Theory, 55 (1988), 183-193.
A. Aziz and W. M. Shah, Inequalities for the polar derivative of a polynomial, Indian J. Pure Appl. Math., 29(2) (1998), 163-173.
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.
A. Cohn, Uber die Anzahl der wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z. 14(1922): 110-148
M. A. Malik, On the derivative of a polynomial, J. Lond. Math. Soc. 1 (1969), 57-60.
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.
W. M. Shah and A. Liman, On some Bernstein type inequalities for polynomials, Nonlinear Funct. Anal. Appl,, 2 (2004), 223-232.
W.M. Shah, A Generalization of a Theorem of Paul Turan, Journal of Ramanujan Society, 1(1996), 29-35.
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).