THE SHARP BOUNDS OF THE SECOND AND THIRD HANKEL DETERMINANTS FOR THE CLASS SL

被引:47
作者
Banga, Shagun [1 ]
Kumar, S. Sivaprasad [1 ]
机构
[1] Delhi Technol Univ, Dept Appl Math, Delhi 110042, India
关键词
Hankel determinant; Lemniscate of Bernoulli; Caratheodory coefficients; Zalcman functional; STARLIKE; COEFFICIENT; LEMNISCATE; KIND;
D O I
10.1515/ms-2017-0398
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Caratheodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H-3(1) and H-2(3) for the well known class SL* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: vertical bar a(3)(2) - a(5)vertical bar for the class SL* is also estimated. Further, a couple of interesting results of SL* are also discussed. (C) 2020 Mathematical Institute Slovak Academy of Sciences
引用
收藏
页码:849 / 862
页数:14
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