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Third Hankel determinant for univalent starlike functions

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper we obtain the bound of the third Hankel determinant

$$\begin{aligned} H_3(1) = \left| \begin{array}{c@{\quad }c@{\quad }c} 1 &{} a_2&{} a_3\\ a_2 &{} a_3&{} a_4\\ a_3 &{} a_4&{} a_5\\ \end{array} \right| \end{aligned}$$

for the class \({\mathcal {S}}^*\) of univalent starlike functions, i.e. the functions which satisfy in the unit disk the condition \({{\,\mathrm{Re}\,}}\frac{zf'(z)}{f(z)}>0\). In our research we apply the correspondence between starlike functions and Schwarz functions and the results obtained by Prokhorov and Szynal and by Carlson.

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Funding

The project/research was financed in the framework of the project Lublin University of Technology-Regional Excellence Initiative, funded by the Polish Ministry of Science and Higher Education (contract no. 030/RID/2018/19).

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618, Lublin, Poland

    Paweł Zaprawa

  2. Department of Mathematics, Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, Belgrade, 11000, Serbia

    Milutin Obradović

  3. Department of Mathematics and Informatics, Faculty of Mechanical Engineering, Ss. Cyril and Methodius University in Skopje, Karpoš II b.b., 1000, Skopje, Republic of North Macedonia

    Nikola Tuneski

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  1. Paweł Zaprawa
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  2. Milutin Obradović
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  3. Nikola Tuneski
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Correspondence to Paweł Zaprawa.

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Zaprawa, P., Obradović, M. & Tuneski, N. Third Hankel determinant for univalent starlike functions. RACSAM 115, 49 (2021). https://doi.org/10.1007/s13398-020-00977-2

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