scholarly journals Certain estimates of Turán’s-type for the maximum modulus of the polar derivative of a polynomial

2020 ◽  
Vol 108 (122) ◽  
pp. 121-130
Author(s):  
Gradimir Milovanovic ◽  
Abdullah Mir ◽  
Abrar Ahmad
Keyword(s):  
Lower Bound ◽  
Unit Disk ◽  
Maximum Modulus ◽  
Uniform Norm ◽  
Polar Derivative ◽  
Derivative Of A Polynomial

We establish some lower bound estimates for the maximum modulus of the polar derivative of a polynomial on the unit disk under the assumption that the polynomial has all zeros in another disk. The obtained results sharpen as well as generalize some estimates of Turan?s-type that relate the uniform-norm of the polar derivative and the 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 Norm and Essential Norm of Composition Followed by Differentiation from Logarithmic Bloch Spaces toHμ∞

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Shanli Ye
Keyword(s):  
Lower Bound ◽  
Unit Disk ◽  
Weighted Space ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces

In this note we express the norm of composition followed by differentiationDCφfrom the logarithmic Bloch and the little logarithmic Bloch spaces to the weighted spaceHμ∞on the unit disk and give an upper and a lower bound for the essential norm of this operator from the logarithmic Bloch space toHμ∞.

Estimates for the uniform norm of complex polynomials in the unit disk

2010 ◽  
Vol 283 (2) ◽  
pp. 193-199 ◽  
Author(s):  
Richard Fournier ◽  
Gérard Letac ◽  
Stephan Ruscheweyh
Keyword(s):  
Unit Disk ◽  
Uniform Norm ◽  
Complex Polynomials

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
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