DOI: 10.12732/ijam.v37i3.7
THIRD ORDER HANKEL DETERMINANT
FOR INVERSE FUNCTIONS OF A CLASS
OF STARLIKE FUNCTIONS OF ORDER \alpha
Elena Karamazova Gelova 1,§ , Nikola Tuneski 2
1 Faculty of Computer Science, Goce Delcev University
Krste Misirkov No. 10-A Stip
Republic of NORTH MACEDONIA
2 Faculty of Mechanical Engineering
Ss. Cyril and Methodius University
Karpo.s II b.b., 1000 Skopje
Republic of NORTH MACEDONIA
Abstract. The main goal of this paper is to determine an upper bound for the third Hankel determinant for the inverse functions of f, belonging to the class of starlike function of order \alpha (0 < \alpha < ½).
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to cite this paper?
DOI: 10.12732/ijam.v37i3.7
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 3
References
[1] M.B. Ahamed and P.P. Roy, The third Hankel determinant for inverse coefficients
of starlike function of order 1/2, Submitted, arXiv:2307.02746v1.
[2] U. Grenander and G. Szego, Toeplitz Forms and Their Applications, California
Monographs in Mathematical Sciences, University of California Press, Berkeley-Los Angeles (1958).
[3] O.S. Kwon, A. Lecko and Y.J. Sim, On the fourth coefficient of functions in the Caratheodory class, Comput. Methods Funct. Theory, 18, No 6 (2018), 307314.
[4] D.V. Krishna and T. Ramreddy, Hankel determinant for starlike and convex functions of order alpha, Tbilisi Mathematical Journal, 5, No 1 (2012), 6576.
[5] A. Lecko, Y.J. Sim and B. Smiarowska, The sharp bound of the Hankel determinant of the third kind for starlike function of order 1/2, Complex Anal. Oper. Theory, 13, No 6 (2019), 22312238.
[6] M. Obradovic and N. Tuneski, On the third order Hankel determinant for inverse functions of certain classes of univalent functions, Eur. J. Math. Appl., 2, No 2 (2022), 17.
[7] M. Obradovic and N. Tuneski, Hankel determinant of second order for inverse functions of certain classes of univalent functions, Advances in Mathematics: Scientific Journal, 12, No 4 (2023), 519528.
[8] B. Rath, K.S. Kumar, D.V. Krishna and A. Lecko, The sharp bound of the Hankel determinant for starlike functions of order 1/2, Complex Anal. and Oper. Theory, 16, No 5
(2022); https://link.springer.com/article/10.1007/s11785-022-01241-8
[9] M. Raza, A. Riaz and D.K. Thomas, The third Hankel determinant for inverse coefficients of convex functions, Bull. Aust. Math. Soc., 109, No 1 (2024), 94100.
[10] L. Shi, H.M. Srivastava, A. Rafiq, M. Arif and M. Ihsan, Results on Hankel determinants for the inverse of certain analytic functions subordinated to the exponential function, Mathematics, 10, No 19 (2022); https://doi.org/10.3390/math10193429
[11] Y.J. Sim, D.K. Thomas and P. Zaprawa, The second Hankel determinant for starlike and convex functions of order alpha, Complex Var. Elliptic Equ., 67, No 10 (2022), 24232443.
[12] D. K. Thomas, N. Tuneski and A. Vasudevarao, Univalent Functions, De Gruyter Studies in Mathematics (2018).
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