Fekete-Szegö problem for generalized bi-subordinate functions of complex order

Year 2020, Volume: 49 Issue: 5, 1695 - 1705, 06.10.2020

Sercan Kazımoğlu , Erhan Deniz

https://doi.org/10.15672/hujms.557072

Cited By: 10

Abstract

In this paper, we obtain the Fekete-Szegö inequality for the generalized bi-subordinate functions of complex order. The various results, which are presented in this paper, would generalize those in related works of several earlier authors.

******************************************************************************************************************************

******************************************************************************************************************************

******************************************************************************************************************************

Keywords

Analytic functions, Starlike functions, Convex functions, Ma-Minda starlike functions, Ma-Minda convex functions, Subordination, Fekete-Szegö Inequaliy

References

• [1] R.M. Ali, S.K. Lee, V. Ravichandran, and S. Supramaniam, Coefficient estimates for bi-univalent Ma–Minda starlike and convex functions, Appl. Math. Lett. 25, 344–351, 2012.
• [2] D.A. Brannan, and T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babe-Bolyai Math. 31, 70-77, 1986.
• [3] S. Bulut, Coefficient estimates for a subclass of parabolic bi-starlike functions, Afr. Math. 29, 331-338, 2018.
• [4] M. Çağlar, H. Orhan and N. Yağmur, Coefficient bounds for new subclasses of biunivalent functions, Filomat 27, 1165-1171, 2013.
• [5] E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. 2, 49–60, 2013.
• [6] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24, 1569–1573, 2011.
• [7] J.M. Jahangiri and S.G. Hamidi, Coefficient estimates for certain classes of biunivalent functions, Int. J. Math. Math. Sci. Article ID 190560, 4 pp. 2013.
• [8] J.M. Jahangiri, S.G. Hamidi and S.A. Halim, Coefficients of bi-univalent functions with positive real part derivatives, Bull. Malay. Math. Sci. Soc. 37, 633-640, 2014.
• [9] J.M. Jahangiri, N. Magesh and J. Yamini, Fekete–Szegö inequalities for classes of bi-starlike and bi-convex functions, Electron. J. Math. Anal. Appl. 3, 133–140, 2015.
• [10] F.R. Keogh and E.P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20, 8–12, 1969.
• [11] S.S. Kumar, V. Kumar and V. Ravichandran, Estimates for the initial coefficients of bi-univalent functions, Tamsui Oxford J. Inform. Math. Sci. 29, 487–504, 2013.
• [12] W.C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis, Tianjin, 1992; Conf. Proc. Lecture. Notes Anal. I, Int Press, Cambridge, MA, 157–169, 1994.
• [13] H. Orhan, N. Magesh and V.K. Balaji, Fekete–Szegö problem for certain classes of Ma-Minda bi-univalent functions, Afr. Math. 27, 889–897, 2016.
• [14] V. Ravichandran, Y. Polatoğlu, M. Bolcal and A. Şen, Certain subclasses of starlike and convex functions of complex order, Hacettepe J. Math. Stat. 34, 9–15, 2005.
• [15] H.M. Srivastava, S. Bulut, M. Çağlar and N. Yağmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27, 831-842, 2013.
• [16] H.M. Srivastava, S.S Eker, and R.M. Ali, Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat 29, 1839–1845, 2015.
• [17] H.M. Srivastava, A.K. Mishra, and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23, 1188–1192, 2010.
• [18] Q.H. Xu, Y.C. Gui and H.M. Srivastava, Coefficient estimates for certain subclasses of analytic functions of complex order, Taiwanese J. Math. 15, 2377-2386, 2011.
• [19] Q.H. Xu, Y.C. Gui and H.M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25, 990–994, 2012.
• [20] Q.H. Xu, H.G. Xiao and H.M Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218, 11461–11465, 2012.
• [21] P. Zaprawa, Estimates of Initial Coefficients for Bi-Univalent Functions, Abst. Appl. Anal. Article ID 357480, 6 pp. 2014.
• [22] P. Zaprawa, On the Fekete–Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21, 169–178, 2014.