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.
(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.āHalim, S. A.āDarus, M.: Hankel determinant for starlike and convex functions, Int. J. Math. Anal. 1(13) (2007), 619ā225.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] ObradoviÄ, M.āPonnusamy, S.: New criteria and distortion theorems for univalent functions, Complex Variables Theory Appl. 44 (2001), 173ā191.10.1080/17476930108815354Search in Google Scholar
[6] ObradoviÄ, M.āPonnusamy, 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. 11ā26.Search in Google Scholar
[7] ObradoviÄ, M.āPonnusamy, S.āWirths, K. J.: Geometric studies on the class š¤(Ī»), Bull. Malays. Math. Sci. Soc. 39(3) (2016), 1259ā1284.10.1007/s40840-015-0263-5Search in Google Scholar
[8] ObradoviÄ, M.āTuneski, N.: Some properties of the class š¤, Ann. Univ. Mariae Curie-SkÅodowska Sect. A 73(1) (2019), 49ā56.10.17951/a.2019.73.1.49-56Search in Google Scholar
[9] ObradoviÄ, M.āTuneski, 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.āSrivastava, H. M.āArif, M.āHussain, S.āKhan, 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
Ā© 2021 Mathematical Institute Slovak Academy of Sciences