GENERALIZED HANKEL DETERMINANT FOR A GENERAL SUBCLASS OF UNIVALENT FUNCTIONS

Year 2018, Volume: 8 Issue: 1.1, 311 - 317, 01.09.2018

S. Yalçın S. Owa

Abstract

Making use of the generalized Hankel determinant, in this work, we consider a general subclass of univalent functions. Moreover, upper bounds are obtained for  a3

Keywords

Analytic and univalent functions , Fekete-Szeg¨o inequality , Hankel determinant

References

• Bucur, R., Andrei, L. and Breaz, D., (2015), Coefficient bounds and Fekete–Szeg¨o problem for a class of analytic functions defined by using a new differential operator, Appl. Math. Sci., 9, pp. 1355 -1368.
• Ding, S. S., Ling, Y.and Bao, G. J., (1995), Some properties of a class of analytic functions, J. Math. Anal. Appl., 195, pp. 71-81.
• Fekete, M. and Szeg¨o, G., (1933), Eine Bemerkung ¨Uber Ungerade Schlichte Funktionen, J. Lond. Math. Soc., 2, pp. 85-89.
• El-Ashwah, R. and Kanas, S., (2015), Fekete-Szeg¨o inequalities for quasi-subordination functions classes of complex order, Kyungpook Math. J., 55, pp. 679-688.
• Kumar, S. S. and Kumar, V., (2014), On Fekete–Szeg¨o inequality for certain class of analytic functions, Acta Univ. Apulensis Math. Inform., 37, pp. 211-222.
• Kowalczyk, B. and Lecko, A., (2015), Fekete–Szeg¨o problem for a certain subclass of close-to-convex functions, Bull. Malays. Math. Sci. Soc., 3, pp. 1393-1410.
• Noonan, J. W. and Thomas, D. K., (1976), On the second Hankel determinant of areally mean p-valent functions, Trans. Amer. Math. Soc., 223, pp. 337–346.
• Noor, K. I., (1983), Hankel determinant problem for the class of functions with bounded boundary rotation, Rev. Roum. Math. Pures Et. Appl., 28, pp. 731-739.
• Hayami, T. and Owa, S., (2009), Hankel determinant for p-valently starlike and convex functions of order α, General Math., 17, pp. 29-44.
• Hayami, T. and Owa, S., (2010), Generalized Hankel determinant for certain classes, Int. Journal ofMath. Analysis, 4, pp. 2473-2585.