Inequalities for the Coefficients of Schwarz Functions
Artykuł w czasopiśmie
MNiSW
70
Lista 2023
| Status: | |
| Autorzy: | Zaprawa Paweł |
| Dyscypliny: | |
| Aby zobaczyć szczegóły należy się zalogować. | |
| Rok wydania: | 2023 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Numer czasopisma: | 4 |
| Wolumen/Tom: | 46 |
| Numer artykułu: | 144 |
| Strony: | 1 - 14 |
| Web of Science® Times Cited: | 1 |
| Scopus® Cytowania: | 1 |
| Bazy: | Web of Science | Scopus |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | TAK |
| Licencja: | |
| Sposób udostępnienia: | Witryna wydawcy |
| Wersja tekstu: | Ostateczna wersja opublikowana |
| Czas opublikowania: | W momencie opublikowania |
| Data opublikowania w OA: | 17 czerwca 2023 |
| Abstrakty: | angielski |
| The relation between a considered family of analytic functions and the class P of functions with a positive real part is one of the main tools used in solving various extremal problems, among others coefficient problems. Another approach can be useful in solving such tasks. This approach is to exploit the correspondence between a considered family and the family B0 of bounded analytic functions ω such that ω(0)=0. Such functions appear in the well-known Schwarz lemma, so they are called Schwarz functions. In the literature, there are numerous coefficient functionals discussed for functions in P. On the other hand, relative functionals for functions in B0 are not so commonly studied. Consequently, we do not know so much about coefficient inequalities for Schwarz functions. We shall fill the gap to some extent considering two types of functionals. The first one is a Zalcman-type functional cn−ckcn−k; the other one is the Hankel determinant cn−1cn+1−cn2. For these functionals, bounds with respect to a fixed first coefficient c1 (or a few initial coefficients) are obtained. Some generalizations of these functionals are also given. All results are sharp. |
