Upper bound of second Hankel determinant for certain subclasses of analytic functions. (English) Zbl 1474.30088
Summary: In this present investigation, we first give a survey of the work done so far in this area of Hankel determinant for univalent functions. Then the upper bounds of the second Hankel determinant \(| a_2 a_4 - a_3^2 |\) for functions belonging to the subclasses \(S(\alpha, \beta)\), \(K(\alpha, \beta)\), \(S_s^\ast(\alpha, \beta)\), and \(K_s(\alpha, \beta)\) of analytic functions are studied. Some of the results, presented in this paper, would extend the corresponding results of earlier authors.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
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