Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions

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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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, close-to-convex 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 Fekete-Szego 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 1-3. 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
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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