Open AccessGeneralizations of some Zygmund-type integral inequalities for polar derivatives of a complex polynomial
Author(s) -
Abdullah Mir
Publication year - 2021
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/pim2124057m
Subject(s) - mathematics , polynomial , polar , norm (philosophy) , complex plane , algebraic number , type (biology) , pure mathematics , inequality , derivative (finance) , algebra over a field , mathematical analysis , physics , ecology , astronomy , political science , financial economics , law , economics , biology
We prove some results for algebraic polynomials in the complex plane that relate the L-norm of the polar derivative of a complex polynomial and the polynomial under some conditions. The obtained results include several interesting generalizations of some Zygmund-type integral inequalities for polynomials and derive polar derivative analogues of some classical Bernsteintype inequalities for the sup-norms on the unit disk as well.