Open AccessSome integral inequalities for the polar derivative of polynomials
Author(s) -
Prasanna Kumar
Publication year - 2019
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim1920085k
Subject(s) - mathematics , generalization , polar , polynomial , degree (music) , inequality , combinatorics , derivative (finance) , pure mathematics , algebra over a field , mathematical analysis , physics , astronomy , acoustics , financial economics , economics
As a generalization of well-known result due to Turan [24] for polynomials having all their zeros in |z| ? 1, Malik [17] proved that, if P(z) is a polynomial of degree n, having all its zeros in |z| ? 1, then for any ? > 0, n{?2?0|P(ei?)|?d?}1/? ? {?2?0|1+ei?|?d?}1/? max |z|=1 |P?(z)|. We generalize the above inequality to polar derivatives, which as special cases include several known results in this area. Besides the paper contains some more results that generalize and sharpen several results known in this direction.