Some Bounds for the Polar Derivative of a Polynomial
Joint Authors
Somsuwan, Jiraphorn
Nakprasit, Keaitsuda Maneeruk
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-03-01
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Abstract EN
The polar derivative of a polynomial p ( z ) of degree n with respect to a complex number α is a polynomial n p ( z ) + α - z p ′ ( z ) , denoted by D α p ( 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 D α p ( z ) on z = R .
Furthermore, we present an upper bound of modulus of D α p ( 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.
American Psychological Association (APA)
Somsuwan, Jiraphorn& Nakprasit, Keaitsuda Maneeruk. 2018. Some Bounds for the Polar Derivative of a Polynomial. International Journal of Mathematics and Mathematical Sciences،Vol. 2018, no. 2018, pp.1-4.
https://search.emarefa.net/detail/BIM-1173485
Modern Language Association (MLA)
Somsuwan, Jiraphorn& Nakprasit, Keaitsuda Maneeruk. Some Bounds for the Polar Derivative of a Polynomial. International Journal of Mathematics and Mathematical Sciences No. 2018 (2018), pp.1-4.
https://search.emarefa.net/detail/BIM-1173485
American Medical Association (AMA)
Somsuwan, Jiraphorn& Nakprasit, Keaitsuda Maneeruk. Some Bounds for the Polar Derivative of a Polynomial. International Journal of Mathematics and Mathematical Sciences. 2018. Vol. 2018, no. 2018, pp.1-4.
https://search.emarefa.net/detail/BIM-1173485
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1173485