Generalizations of some Zygmund-type integral inequalities for polar derivatives of a complex polynomial | Zendy

Abdullah Mir | Zendy

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Generalizations 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 mathematique

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.

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