Third Order Hankel Determinant for Inverse Functions of a Classes of Univalent Functions with Bounded Turning
Main Article Content
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 two classes of univalent functions with bounded turning.
Article Details
References
- M.B. Ahamed, P.P. Roy, The Third Hankel Determinant for Inverse Coefficients of Starlike Functions of Order 1/2, arXiv:2307.02746 [math.CV] (2023). https://doi.org/10.48550/ARXIV.2307.02746.
- D.V. Krishna, T. Ramreddy, Hankel Determinant for Starlike and Convex Functions of Order Alpha, Tbilisi Math. J. 5 (2012), 65–76. https://doi.org/10.32513/tbilisi/1528768890.
- A. Lecko, Y.J. Sim, B. Smiarowska, The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Func- ´ tions of Order 1/2, Complex Anal. Oper. Theory 13 (2019), 2231–2238. https://doi.org/10.1007/s11785-018-0819-0.
- M. Obradovi´c, N. Tuneski, On the Third Order Hankel Determinant for Inverse Functions of Certain Classes of Univalent Functions, Eur. J. Math. Appl. 2 (2022), 2. https://doi.org/10.28919/ejma.2022.2.2.
- M. Obradovic, N. Tuneski, Hankel Determinant of Second Order for Inverse Functions of Certain Classes of Univalent Functions, Adv. Math.: Sci. J. 12 (2023), 519–528. https://doi.org/10.37418/amsj.12.4.2.
- B. Rath, K.S. Kumar, D.V. Krishna, A. Lecko, The Sharp Bound of the Third Hankel Determinant for Starlike Functions of Order 1/2, Complex Anal. Oper. Theory 16 (2022), 65. https://doi.org/10.1007/s11785-022-01241-8.
- M. Raza, A. Riaz, D.K. Thomas, The Third Hankel Determinant for Inverse Coefficients of Convex Functions, Bull. Aust. Math. Soc. 109 (2024), 94–100. https://doi.org/10.1017/S0004972723000357.
- L. Shi, H.M. Srivastava, A. Rafiq, M. Arif, M. Ihsan, Results on Hankel Determinants for the Inverse of Certain Analytic Functions Subordinated to the Exponential Function, Mathematics 10 (2022), 3429. https://doi.org/10.3390/math10193429.
- Y.J. Sim, D.K. Thomas, P. Zaprawa, The Second Hankel Determinant for Starlike and Convex Functions of Order Alpha, Complex Var. Elliptic Equ. 67 (2022), 2423–2443. https://doi.org/10.1080/17476933.2021.1931149.
- A. Janteng, S.A. Halim, M. Darus, Coefficient Inequality for a Function Whose Derivative Has a Positive Real Part, J. Inequal. Pure Appl. Math. 7 (2006), 50.
- K. Khatter, V. Ravichandran, S.S. Kumar, Third Hankel Determinant of Starlike and Convex Functions, J. Anal. 28 (2020), 45–56. https://doi.org/10.1007/s41478-017-0037-6.
- M. Obradovi´c, N. Tuneski, Upper Bounds of the Third Hankel Determinant for Classes of Univalent Functions With Bounded Turning, preprint, arXiv:2004.04960 [math.CV]. https://doi.org/10.48550/arXiv.2004.04960.
- D. Prokhorov, J. Szynal, Inverse Coefficients for (α, β)-Convex Functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 35 (1981), 125–143.
- F. Carlson, Sur les Coeffcients D’une Fonction Bornee dans le Cercle Unite, Ark. Mat. Astr. Fys. 27 (1940), 8.
- A.W. Goodman, Univalent Functions, Mariner Publ. Co, Tampa, 1983.
- E. Karamazova Gelova, N. Tuneski, Third Order Hankel Determinant for Inverse Functions of a Classof Starlike Functions of Order α, Int. J. Appl. Math. 37 (2024), 369–381. https://doi.org/10.12732/ijam.v37i3.7.