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Hankel determinants of second and third order for the class š“¢ of univalent functions

  • Milutin Obradović and Nikola Tuneski EMAIL logo
Published/Copyright: June 8, 2021
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Abstract

In this paper we give the upper bounds of the Hankel determinants of the second and third order for the class š“¢ of univalent functions in the unit disc.

MSC 2010: 30C45; 30C50; 30C55
  1. (Communicated by Stanis lawa Kanas )

References

[1] Dienes, P.: The Taylor Series: An Introduction to the Theory of Functions of a Complex Variable, New York-Dover: Mineola, NY, USA, 1957.Search in Google Scholar

[2] Duren, P. L.: Univalent Function, Springer-Verlag, New York, 1983.Search in Google Scholar

[3] Janteng, A.—Halim, S. A.—Darus, M.: Hankel determinant for starlike and convex functions, Int. J. Math. Anal. 1(13) (2007), 619–225.Search in Google Scholar

[4] Lebedev, N. A.: Area Principle in the Theory of Univalent Functions, Nauka, Moscow, 1975 (in Russian).Search in Google Scholar

[5] Obradović, M.—Ponnusamy, S.: New criteria and distortion theorems for univalent functions, Complex Variables Theory Appl. 44 (2001), 173–191.10.1080/17476930108815354Search in Google Scholar

[6] Obradović, M.—Ponnusamy, S.: On the class š“¤, Proc. 21st Annual Conference of the Jammu Math. Soc. and a National Seminar on Analysis and its Application, 2011, pp. 11–26.Search in Google Scholar

[7] Obradović, M.—Ponnusamy, S.—Wirths, K. J.: Geometric studies on the class š“¤(Ī»), Bull. Malays. Math. Sci. Soc. 39(3) (2016), 1259–1284.10.1007/s40840-015-0263-5Search in Google Scholar

[8] Obradović, M.—Tuneski, N.: Some properties of the class š“¤, Ann. Univ. Mariae Curie-Skłodowska Sect. A 73(1) (2019), 49–56.10.17951/a.2019.73.1.49-56Search in Google Scholar

[9] Obradović, M.—Tuneski, N.: New upper bounds of the third Hankel determinant for some classes of univalent functions, submitted, https://arxiv.org/abs/1911.10770.Search in Google Scholar

[10] Shi, L.—Srivastava, H. M.—Arif, M.—Hussain, S.—Khan, H.: An investigation of the third Hankel determinant problem for certain subfamilies of univalent functions involving the exponential function, Symmetry 11 (2019), 598.10.3390/sym11050598Search in Google Scholar

Received: 2020-01-20
Accepted: 2020-09-14
Published Online: 2021-06-08
Published in Print: 2021-06-25

Ā© 2021 Mathematical Institute Slovak Academy of Sciences

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