Mathematica Pannonica
Volume/Issue:
Volume 27_NS1: Issue 2
Hankel Determinant of Second Order for Some Classes of Analytic Functions
Authors:
Milutin ObradovićDepartment of Mathematics, Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000, Belgrade, Serbia

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Nikola TuneskiDepartment 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

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Pages:
89–94
Online Publication Date:
06 Oct 2021
Publication Date:
18 Nov 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2021.00009
Keywords:
analytic; univalent; Hankel determinant; starlike of order α; Ozaki close-to-convex functions
Open access

Let ƒ be analytic in the unit disk B and normalized so that ƒ (z) = z + a2z2 + a3z3 +܁܁܁. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order α, Ozaki close-to-convex functions and two other classes of analytic functions. Some of the estimates are sharp.

  • [1]

    Bello, R., and Opoola, T. Upper bounds for fekete-szego functions and the second hankel determinant for a class of starlike functions. IOSR Journal of Mathematics 12, 2 (2017), 34–39.

    • Search Google Scholar
    • Export Citation
  • [2]

    Duren, P. L. Univalent functions, vol. 259 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, New York, 1983.

    • Search Google Scholar
    • Export Citation
  • [3]

    Kargar, R., and Ebadian, A. Ozaki’s conditions for general integral operator. Sahand Communications in Mathematical Analysis 5, 1 (2017), 61–67.

    • Search Google Scholar
    • Export Citation
  • [4]

    Nunokawa, M., Saitoh, H., Ikeda, A., Koike, N., and Ota, Y. On certain starlike functions. No. 963. 1996, pp. 74–77. Univalent functions and the Briot-Bouquet differential equations (Japanese) (Kyoto, 1996).

    • Search Google Scholar
    • Export Citation
  • [5]

    Obradovich, M., Ponnusami, S., and Virts, K.-u. Characteristics of the coefficients and partial sums of some univalent functions. Sibirsk. Mat. Zh. 54, 4 (2013), 852–870.

    • Search Google Scholar
    • Export Citation
  • [6]

    Ozaki, S. On the theory of multivalent functions. II. Sci. Rep. Tokyo Bunrika Daigaku. Sect. A 4 (1941), 45–87.

  • [7]

    Prokhorov, D. V., and Szynal, J. Inverse coefficients for (a, β)-convex functions. Ann. Univ. Mariae Curie-Skłodowska Sect. A 35 (1981), 125–143 (1984).

    • Search Google Scholar
    • Export Citation
  • [8]

    Sakaguchi, K. A property of convex functions and an application to criteria for univalence. Bull. Nara Univ. Ed. Natur. Sci. 22, 2 (1973), 1–5.

    • Search Google Scholar
    • Export Citation
  • [9]

    Singh, R., and Singh, S. Some sufficient conditions for univalence and starlikeness. Colloq. Math. 47, 2 (1982), 309–314 (1983).

  • [10]

    Sokól, J., and Thomas, D. K. The second Hankel determinant for alpha-convex functions. Lith. Math. J. 58, 2 (2018), 212–218.

  • [11]

    Thomas, D. K., Tuneski, N., and Vasudevarao, A. Univalent functions, vol. 69 of De Gruyter Studies in Mathematics. De Gruyter, Berlin, 2018. A primer.

    • Search Google Scholar
    • Export Citation
  • [12]

    Umezawa, T. Analytic functions convex in one direction. J. Math. Soc. Japan 4 (1952), 194–202.

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM (Akadémiai Kiadó, Budapest)
  • György GÁT (University of Debrecen)

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Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
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ltoth@gamma.ttk.pte.hu

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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