Mathematics and Statistics Vol. 8(5), pp. 566 - 569
DOI: 10.13189/ms.2020.080510
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Hankel Determinant H₂(3) for Certain Subclasses of Univalent Functions

Andy Liew Pik Hern ^1,*, Aini Janteng ¹, Rashidah Omar ^2
1 Faculty of Science and Natural Resources, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah, Malaysia
² Faculty of Computer and Mathematical Sciences, Universiti Teknologi Mara Cawangan Sabah, 88997 Kota Kinabalu, Sabah, Malaysia

ABSTRACT

Let S to be the class of functions which are analytic, normalized and univalent in the unit disk . 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 , and K_S 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 and is defined by . is greatly familiar so called Fekete-Szeg¨o functional. It has been discussed since 1930's. Mathematicians still have lots of interest to this, especially in an altered version of . 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 has not been discussed in many times yet. In this article, we deal with this Hankel determinant . From this determinant, it consists of coefficients of function f which belongs to the classes and K_S so we may find the bounds of for these classes. Likewise, we got the sharp results for and K_s for which a₂ = 0 are obtained.

KEYWORDS
Univalent Functions, Starlike Functions w.r.t. Symmetric Points, Convex Functions w.r.t. Symmetric Points, Hankel Determinant

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Andy Liew Pik Hern , Aini Janteng , Rashidah Omar , "Hankel Determinant H₂(3) for Certain Subclasses of Univalent Functions," Mathematics and Statistics, Vol. 8, No. 5, pp. 566 - 569, 2020. DOI: 10.13189/ms.2020.080510.

(b). APA Format:
Andy Liew Pik Hern , Aini Janteng , Rashidah Omar (2020). Hankel Determinant H₂(3) for Certain Subclasses of Univalent Functions. Mathematics and Statistics, 8(5), 566 - 569. DOI: 10.13189/ms.2020.080510.