IJAM: Volume 37, No. 3 (2024)

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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How to cite this paper?
DOI: 10.12732/ijam.v3
7i3.7
Source: 
International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 202
4
Volume: 3
7
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), 307–314.

[4] D.V. Krishna and T. Ramreddy, Hankel determinant for starlike and convex functions of order alpha, Tbilisi Mathematical Journal, 5, No 1 (2012), 65–76.

[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), 2231–2238.

[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), 1–7.

[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), 519–528.

[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), 94–100.

[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), 2423–2443.

[12] D. K. Thomas, N. Tuneski and A. Vasudevarao, Univalent Functions, De Gruyter Studies in Mathematics (2018).

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