Inequalities for the Polar Derivative of a Polynomial | Zendy

Ahmad Zireh | Zendy

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Inequalities for the Polar Derivative of a Polynomial

Author(s) -

Ahmad Zireh

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/181934

Subject(s) - mathematics , polynomial , combinatorics , degree (music) , operator (biology) , mathematical analysis , physics , chemistry , biochemistry , repressor , acoustics , transcription factor , gene

For a polynomial () of degree , we consider an operator which map a polynomial () into ()∶=(−)′()+() with respect to . It was proved by Liman et al. (2010) that if () has no zeros in ||<1, then for all ,∈ℂ with ||≥1,||≤1 and ||=1, |()+((||−1)/2)()|≤(/2){[|+((||−1)/2)|+|+((||−1)/2)|]max||=1|()|−[|+((||−1)/2)|−|+((||−1)/2)|]min||=1|()|}. In this paper we extend the above inequality for the polynomials having no zeros in ||<, where ≤1. Our result generalizes certain well-known polynomial inequalities

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