Some Upper Bound Estimates for the Maximal Modulus of the Polar Derivative of a Polynomial

2020 ◽  
Vol 55 (3) ◽  
pp. 189-195
Author(s):  
A. Mir ◽  
M. Ibrahim Sheikh
Keyword(s):  
Upper Bound ◽  
Polar Derivative ◽  
Maximal Modulus ◽  
Derivative Of A Polynomial

scholarly journals Some Bounds for the Polar Derivative of a Polynomial

2018 ◽  
Vol 2018 ◽  
pp. 1-4
Author(s):  
Jiraphorn Somsuwan ◽  
Keaitsuda Maneeruk Nakprasit
Keyword(s):  
Lower Bound ◽  
Complex Number ◽  
Upper Bound ◽  
Polar Derivative ◽  
Derivative Of A Polynomial

The polar derivative of a polynomial p(z) of degree n with respect to a complex number α is a polynomial np(z)+α-zp′(z), denoted by Dαp(z). Let 1≤R≤k. For a polynomial p(z) of degree n having all its zeros in z≤k, we investigate a lower bound of modulus of Dαp(z) on z=R. Furthermore, we present an upper bound of modulus of Dαp(z) on z=R for a polynomial p(z) of degree n having no zero in z<k. In particular, our results in case R=1 generalize some well-known inequalities.

scholarly journals Some Lp Inequalities for the Polar Derivative of a Polynomial

2001 ◽  
Vol 254 (2) ◽  
pp. 618-626 ◽  
Author(s):  
N.K Govil ◽  
Griffith Nyuydinkong ◽  
Berhanu Tameru
Keyword(s):  
Polar Derivative ◽  
Derivative Of A Polynomial

scholarly journals A note on the zeros of polar derivative of a polynomial

2020 ◽  
Vol 8 (2) ◽  
pp. 405-413
Author(s):  
Praveen Kumar K. ◽  
Krishna Reddy B.
Keyword(s):  
Polar Derivative ◽  
Derivative Of A Polynomial

scholarly journals Zygmund’s Type Inequality to the Polar Derivative of a Polynomial

2016 ◽  
Vol 5 ◽  
pp. 52-59
Author(s):  
M.S. Pukhta
Keyword(s):  
Type Inequality ◽  
Polar Derivative ◽  
Zygmund’S Inequality ◽  
Derivative Of A Polynomial

In this paper we improve a result recently proved by Irshad et al. [On the Inequalities Concerning to the Polar Derivative of a Polynomial with Restricted Zeroes, Thai Journal of Mathematics, 2014 (Article in Press)] and also extend Zygmund's inequality to the polar derivative of a polynomial.

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