SECOND HANKEL DETERMINAT FOR CERTAIN ANALYTIC FUNCTIONS SATISFYING SUBORDINATE CONDITION

被引：7

作者：

Deniz, Erhan ^{[1
]}

Budak, Levent ^{[1
]}

机构：

[1] Kafkas Univ, Fac Sci & Letters, Dept Math, Kars, Turkey

来源：

MATHEMATICA SLOVACA | 2018年 / 68卷 / 02期

关键词：

analytic functions; starlike functions; convex functions; Ma-Minda starlike functions; Ma-Minda convex functions; subordination; second Hankel determinant; FEKETE-SZEGO PROBLEM; COMPLEX-ORDER; SUBCLASSES; STARLIKE;

D O I：

10.1515/ms-2017-0116

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce and investigate the following subclass 1 + 1/gamma (zf'(z) + lambda z(2) f ''(z)/lambda z f'(z) + (1 - lambda)f(z) - 1) (sic) phi(z) (0 <= lambda <= 1, gamma is an element of C \ {0}) of analytic functions, phi is an analytic function with positive real part in the unit disk D satisfying phi(0) = 1, phi'(0) > 0, and phi(D) is symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant vertical bar a(2)a(4) - a(3)(2)vertical bar ail for functions belonging to the this class is studied using Toeplitz determinants. The results, which are presented in this paper, would generalize those in related works of several earlier authors. (C) 2018 Mathematical Institute Slovak Academy of Sciences

引用

页码：463 / 471

页数：9

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