Andy Liew Pik Hern, and Aini Janteng, and Rashidah Omar, (2020) Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions. Mathematics and Statistics, 8 (5). 566 569.
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Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions.pdf Download (70kB) 

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Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions1.pdf Download (264kB) 
Abstract
Let S to be the class of functions which are analytic, normalized and univalent in the unit disk U = {z : z < 1}. The main subclasses of S are starlike functions, convex functions, closetoconvex functions, quasiconvex functions, starlike functions with respect to (w.r.t.) symmetric points and convex functions w.r.t. symmetric points which are denoted by S ∗ , K, C, C ∗ , S ∗ S , and KS respectively. In recent past, a lot of mathematicians studied about Hankel determinant for numerous classes of functions contained in S. The qth Hankel determinant for q ≥ 1 and n ≥ 0 is defined by Hq(n). H2(1) = a3 − a2 2 is greatly familiar so called FeketeSzego functional. It has been discussed ¨ since 1930’s. Mathematicians still have lots of interest to this, especially in an altered version of a3 − µa2 2 . Indeed, there are many papers explore the determinants H2(2) and H3(1). From the explicit form of the functional H3(1), it holds H2(k) provided k from 13. Exceptionally, one of the determinant that is H2(3) = a3a5 − a4 2 has not been discussed in many times yet. In this article, we deal with this Hankel determinant H2(3) = a3a5 − a4 2 . From this determinant, it consists of coefficients of function f which belongs to the classes S ∗ S and KS so we may find the bounds of H2(3) for these classes. Likewise, we got the sharp results for S ∗ S and KS for which a2 = 0 are obtained.
Item Type:  Article 

Uncontrolled Keywords:  Univalent Functions, Starlike Functions w.r.t. Symmetric Points, Convex Functions w.r.t. Symmetric Points, Hankel Determinant 
Subjects:  Q Science > Q Science (General) 
Divisions:  FACULTY > Faculty of Science and Natural Resources 
Depositing User:  SITI AZIZAH BINTI IDRIS  
Date Deposited:  10 Nov 2020 05:51 
Last Modified:  10 Nov 2020 05:51 
URI:  http://eprints.ums.edu.my/id/eprint/26284 
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