On H3 (1) Hankel determinant for certain subclass of analytic functions

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D. Vamshee Krishna
D. Shalini

Abstract

The objective of this paper is to obtain an upper bound to Hankel determinant of third order for any function f, when it belongs to certain subclass of analytic functions, defined on the open unit disc in the complex plane.

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How to Cite
Vamshee Krishna, D., & Shalini, D. (2020). On H3 (1) Hankel determinant for certain subclass of analytic functions. Extracta Mathematicae, 35(1), 35-42. Retrieved from https://publicaciones.unex.es/index.php/EM/article/view/2605-5686.35.1.35
Section
Function Theory

References

[1] R.M. Ali, Coefficients of the inverse of strongly starlike functions, Bull. Malays. Math. Sci. Soc., (2) 26 (1) (2003), 63 – 71.
[2] K.O. Babalola, On H3 (1) Hankel determinant for some classes of univalent functions, in “Inequality Theory and Applications 6” (ed. Cho, Kim and Dragomir), Nova Science Publishers, New York, 2010, 1 – 7.
[3] D. Bansal, S. Maharana, J.K. Prajapat, Third order Hankel determinant for certain univalent functions, J. Korean Math. Soc. 52 (6) (2015), 1139 – 1148.
[4] L. de Branges, A proof of Bieberbach conjecture, Acta Math. 154 (1-2) (1985), 137 – 152.
[5] N.E. Cho, B. Kowalczyk, O.S. Kwon, A. Lecko, Y.J. Sim, The bounds of some determinants for starlike functions of order Alpha, Bull. Malays. Math. Sci. Soc. 41 (1) (2018), 523 -û 535.
[6] P.L. Duren, “Univalent Functions”, Grundlehren der Mathematischen Wissenschaften, 259, Springer-Verlag, New York, 1983.
[7] R. Ehrenborg, The Hankel determinant of exponential polynomials, Amer. Math. Monthly 107 (6) (2000), 557 – 560.
[8] M. Fekete, G. Szegö, Eine bemerkung uber ungerade schlichte funktionen, J. Lond. Math. Soc. 8 (2) (1933), 85 – 89.
[9] T. Hayami, S. Owa, Generalized Hankel determinant for certain classes, Int. J. Math. Anal. 4 (49-52) (2010), 2573 – 2585.
[10] 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 (2) (2006), Article 50, 1 – 5.
[11] A. Janteng, S.A. Halim, M. Darus, Hankel Determinant for starlike and convex functions, Int. J. Math. Anal. 1 (13-16) (2007), 619 – 625.
[12] B. Kowalczyk, A. Lecko, Y.J. Sim, The sharp bound for the Hankel determinant of the Third kind for convex functions, Bull. Aust. Math. Soc. 97 (3) (2018), 435 – 445.
[13] J.W. Layman, The Hankel transform and some of its properties, J. Integer Seq. 4 (1) (2001), Article 01.1.5, 1 – 11.
[14] A. Lecko, Y.J. Sim, B. Śmiarowska, The Sharp Bound of the Hankel Determinant of the Third kind for starlike functions of order 1/2, Complex Anal. Oper. Theory 13 (5) (2019), 2231 – 2238.
[15] S.K. Lee, V. Ravichandran, S. Supramaniam, Bounds for the second Hankel determinant of certain univalent functions, J. Inequal. Appl. (2013), 2013:281, 1 – 17.
[16] R.J. Libera, E.J. Zlotkiewicz, Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc. 87 (2) (1983), 251 – 257.
[17] A.E. Livingston, The coefficients of multivalent close-to-convex functions, Proc. Amer. Math. Soc. 21 (1969), 545 – 552.
[18] K.I. Noor, Hankel determinant problem for the class of functions with bounded boundary rotation, Rev. Roumaine Math. Pures Appl. 28 (8) (1983), 731 – 739.
[19] H. Orhan, P. Zaprawa, Third Hankel determinants for starlike and convex functions of order alpha, Bull. Korean Math. Soc. 55 (1) (2018), 165 – 173.
[20] Ch. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc. s1-41 (1) (1966), 111 – 122.
[21] Ch. Pommerenke, G. Jensen “Univalent Functions”, Studia Mathematica/Mathematische Lehrbücher 25, Vandenhoeck und Ruprecht, Gottingen, 1975.
[22] M. Raza, S.N. Malik, Upper bound of third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli, J. Inequal. Appl. (2013), 2013:412, 1 – 8.
[23] T.V. Sudharsan, S.P. Vijayalakshmi, B.A. Stephen, Third Hankel determinant for a subclass of analytic functions, Malaya J. Math. 2 (4) (2014), 438 – 444.
[24] D. Vamshee Krishna, T. Ramreddy, Coefficient inequality for certain p-valent analytic functions, Rocky Mountain J. Math. 44 (6) (2014), 1941 – 1959.
[25] P. Zaprawa, Third Hankel determinants for subclasses of univalent functions, Mediterr. J. Math. 14 (1) (2017), Article 19, 1 – 10.
[26] Zhi-Gang Wang, Chun-Yi Gao, Shao-Mou Yuan, On the univalency of certain analytic functions, J. Inequal. Pure Appl. Math. 7 (1) (2006), Article 9, 1 – 4.