Bound on H3(1) Hankel determinant for pre-starlike functions of order α


The objective of this paper is to obtain best possible upper bound to the third Hankel determinant for the pre-starlike functions of order α (0 ≤ α < 1), using Toeplitz determinants.

Biografía del autor

D. Vamshee Krishna, GITAM University.
Departamento de Matemáticas.
D. Shalini, Sri Venkateswara College of Engineering and Technology.
Departamento de Matemáticas.


[1] R. M. Ali, Coefficients of the inverse of strongly starlike functions, Bull. Malays. Math. Sci. Soc., (2nd Series), 26 (1), pp. 63-71, (2003).

[2] K. O. Babalola, On H3(1) Hankel determinant for some classes of univalent functions, Inequality Theory and Applications, 6, pp. 1-7, (2010).

[3] L. de Branges de Bourcia, A proof of Bieberbach conjecture, Acta Mathematica, 154 (1-2), pp. 137-152, (1985).

[4] P. L. Duren, Univalent functions, Vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, (1983).

[5] U. Grenander and G. Szegö, Toeplitz forms and their applications. 2nd ed. New York (NY): Chelsea Publishing Co., (1984).

[6] A. Janteng, S. A. Halim and M. Darus, Hankel Determinant for starlike and convex functions, Int. J. Math. Anal. (Ruse), 1 (13), pp. 619-625, (2007).

[7] R. J. Libera and E. J. Zlotkiewicz, Coefficient bounds for the inverse of a function with derivative in P , Proc. Amer. Math. Soc., 87 (2), pp. 251-257, (1983).

[8] Ch. Pommerenke, Univalent functions, Gottingen: Vandenhoeck and Ruprecht; (1975).

[9] Ch. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc., s1-41 (1), pp. 111-122, (1966).

[10] St. Ruscheweyh, Linear operators between classes of pre-starlike functions, Comm. Math. Helv., 52, pp. 497-509, (1977).

[11] H. Silverman and E. M. Silvia, Pre-starlike functions with negative coefficients, Int. J. Math. Math. Sci., 2 (3), pp. 427-439, (1979).

[12] B. Simon, Orthogonal polynomials on the unit circle, part 1. Classical theory. Vol. 54, American mathematical society colloquium publications. Providence (RI): American Mathematical Society; (2005).

[13] D. Vamshee Krishna and T. RamReddy, Coefficient inequality for parabolic star like functions of order alpha, Afr. Mat., 27 (1-2), pp. 121-132, (2016).

[14] D. Vamshee Krishna and T. RamReddy, An upper bound to the second Hankel determinant for pre-star like functions of order α, Le Matematiche, 70 (2), pp. 109-122, (2015).

[15] D. Vamshee Krishna and T. RamReddy, Coefficient inequality for certain p− valent analytic functions, Rocky Mountain J. Math., 44 (6), pp. 1941-1959, (2014).
Cómo citar
Krishna, D., & Shalini, D. (2018). Bound on H3(1) Hankel determinant for pre-starlike functions of order α. Proyecciones. Revista De Matemática, 37(2), 305-315. Recuperado a partir de