scholarly journals On some inequalities for derivatives of algebraic polynomials in unbounded regions with angles

2021 ◽  
Author(s):  
Cevahir Doğanay GÜN
Keyword(s):  
Algebraic Polynomials ◽  
Derivatives Of

Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials

1996 ◽  
Vol 30 (1-2) ◽  
pp. 79-92
Author(s):  
Theodore Kilgore ◽  
Michael Felten
Keyword(s):  
Algebraic Polynomials ◽  
Derivatives Of

scholarly journals Inequalities for the First and Second Derivatives of Algebraic Polynomials on an Ellipse

2021 ◽  
Author(s):  
Tatiana M. Nikiforova
Keyword(s):  
Special Form ◽  
Algebraic Polynomials ◽  
Second Derivatives ◽  
Derivatives Of

We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.

scholarly journals Generalizations of some Zygmund-type integral inequalities for polar derivatives of a complex polynomial

2021 ◽  
Vol 110 (124) ◽  
pp. 57-69
Author(s):  
Abdullah Mir
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Integral Inequalities ◽  
Complex Polynomial ◽  
Algebraic Polynomials ◽  
Polar Derivative ◽  
Type Integral ◽  
Polar Derivatives ◽  
Derivatives Of

We prove some results for algebraic polynomials in the complex plane that relate the L-norm of the polar derivative of a complex polynomial and the polynomial under some conditions. The obtained results include several interesting generalizations of some Zygmund-type integral inequalities for polynomials and derive polar derivative analogues of some classical Bernsteintype inequalities for the sup-norms on the unit disk as well.

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