The second Hankel determinant for starlike and convex functions of order alpha
Artykuł w czasopiśmie
MNiSW
70
Lista 2021
| Status: | |
| Autorzy: | Sim Young Jae, Thomas Derek K., Zaprawa Paweł |
| Dyscypliny: | |
| Aby zobaczyć szczegóły należy się zalogować. | |
| Rok wydania: | 2022 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Numer czasopisma: | 10 |
| Wolumen/Tom: | 67 |
| Strony: | 2423 - 2443 |
| Web of Science® Times Cited: | 9 |
| Scopus® Cytowania: | 10 |
| Bazy: | Web of Science | Scopus |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | NIE |
| Abstrakty: | angielski |
| In recent years, the study of Hankel determinants for various subclasses of normalised univalent functions f∈S given by f(z)=z+∑∞n=2anzn for D={z∈C:|z|<1} has produced many interesting results. The main focus of interest has been estimating the second Hankel determinant of the form H2,2(f)=a2a4−a23. A non-sharp bound for H2,2(f) when f∈K(α), α∈[0,1) consisting of convex functions of order α was found by Krishna and Ramreddy (Hankel determinant for starlike and convex functions of order alpha. Tbil Math J. 2012;5:65–76), and later improved by Thomas et al. (Univalent functions: a primer. Berlin: De Gruyter; 2018). In this paper, we give the sharp result. Moreover, we obtain sharp results for H2,2(f−1) for the inverse functions f−1 when f∈K(α), and when f∈S∗(α), the class of starlike functions of order α. Thus, the results in this paper complete the set of problems for the second Hankel determinants of f and f−1 for the classes S∗(α), K(α), S∗β and Kβ, where S∗β and Kβ are, respectively, the classes of strongly starlike, and strongly convex functions of order β. |
