scholarly journals On Bernstein-Type Inequalities for Rational Functions with Prescribed Poles

2021 ◽  
Vol 45 (4) ◽  
pp. 615-622
Author(s):  
ABDULLAH MIR ◽  
Keyword(s):  
Rational Functions ◽  
Bernstein Type ◽  
Bernstein Type Inequalities

In this paper, we shall use a parameter β and obtain some Bernstein-type inequalities for rational functions with prescribed poles which generalize the results of Qasim and Liman and Li, Mohapatra and Rodriguez and others.

Inequalities for Rational Functions With Prescribed Poles

1998 ◽  
Vol 50 (1) ◽  
pp. 152-166 ◽  
Author(s):  
G. Min
Keyword(s):  
Type Inequality ◽  
Rational Functions ◽  
Complex Conjugation ◽  
Bernstein Type ◽  
Rational System ◽  
Markov Type ◽  
Classical Polynomials ◽  
Bernstein Type Inequalities

AbstractThis paper considers the rational system Pn(a1, a2,……,an) := with nonreal elements in paired by complex conjugation. It gives a sharp (to constant) Markov-type inequality for real rational functions in Pn(a1, a2,……an). The corresponding Markov-type inequality for high derivatives is established, as well as Nikolskii-type inequalities. Some sharp Markov- and Bernstein-type inequalities with curved majorants for rational functions in Pn(a1, a2,……an) are obtained, which generalize some results for the classical polynomials. A sharp Schur-type inequality is also proved and plays a key role in the proofs of our main results

ON THE KANTOROVICH VARIANT OF GENERALIZED BERNSTEIN TYPE RATIONAL FUNCTIONS

2006 ◽  
Vol 39 (1) ◽  
pp. 117-130
Author(s):  
Vijay Gupta ◽  
Nurhayat İspir
Keyword(s):  
Rational Functions ◽  
Bernstein Type
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