Open AccessEstimates for analytic functions concerned with Hankel determinant
Author(s) -
Bülent Nafi Örnek
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i9.907
Subject(s) - mathematics , analytic function , lemma (botany) , unit disk , mathematical analysis , limit (mathematics) , function (biology) , hankel matrix , hankel transform , pure mathematics , derivative (finance) , boundary (topology) , upper and lower bounds , class (philosophy) , unit (ring theory) , bessel function , ecology , mathematics education , poaceae , evolutionary biology , financial economics , economics , biology , artificial intelligence , computer science
UDC 517.5We give an upper bound of Hankel determinant of the first order for the classes of an analytic function. In addition, an evaluation with the Hankel determinant from below will be given for the second angular derivative of analytic function. For new inequalities, the results of Jack's lemma and Hankel determinant were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of an angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.