Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions
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...
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| Format: | Article |
| Language: | English English |
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2020
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| Online Access: | https://eprints.ums.edu.my/id/eprint/26284/1/Hankel%20Determinant%20H2%283%29%20for%20Certain%20Subclasses%20of%20Univalent%20Functions.pdf https://eprints.ums.edu.my/id/eprint/26284/2/Hankel%20Determinant%20H2%283%29%20for%20Certain%20Subclasses%20of%20Univalent%20Functions1.pdf |
| _version_ | 1825713998953185280 |
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| author | Andy Liew Pik Hern Aini Janteng Rashidah Omar |
| author_facet | Andy Liew Pik Hern Aini Janteng Rashidah Omar |
| author_sort | Andy Liew Pik Hern |
| collection | UMS |
| description | 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. |
| first_indexed | 2024-03-06T03:05:15Z |
| format | Article |
| id | ums.eprints-26284 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:05:15Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ums.eprints-262842021-01-15T08:19:19Z https://eprints.ums.edu.my/id/eprint/26284/ Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions Andy Liew Pik Hern Aini Janteng Rashidah Omar Q Science (General) 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. 2020 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/26284/1/Hankel%20Determinant%20H2%283%29%20for%20Certain%20Subclasses%20of%20Univalent%20Functions.pdf text en https://eprints.ums.edu.my/id/eprint/26284/2/Hankel%20Determinant%20H2%283%29%20for%20Certain%20Subclasses%20of%20Univalent%20Functions1.pdf 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. https://doi.org/10.13189/ms.2020.080510 |
| spellingShingle | Q Science (General) Andy Liew Pik Hern Aini Janteng Rashidah Omar Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions |
| title | Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions |
| title_full | Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions |
| title_fullStr | Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions |
| title_full_unstemmed | Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions |
| title_short | Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions |
| title_sort | hankel determinant h2 3 for certain subclasses of univalent functions |
| topic | Q Science (General) |
| url | https://eprints.ums.edu.my/id/eprint/26284/1/Hankel%20Determinant%20H2%283%29%20for%20Certain%20Subclasses%20of%20Univalent%20Functions.pdf https://eprints.ums.edu.my/id/eprint/26284/2/Hankel%20Determinant%20H2%283%29%20for%20Certain%20Subclasses%20of%20Univalent%20Functions1.pdf |
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