Fekete-Szegö problems for generalized Sakaguchi type functions associated with quasi-subordination
DOI:
https://doi.org/10.24193/subbmath.2018.3.05Keywords:
Analytic functions, subordination, quasi-subordination, Fekete-Szegö inequality, Sakaguchi functions.Abstract
In the present paper, the authors introduce a generalized Sakaguchi type non-Bazilevic function class Mλ,β (φ, s, t) of analytic functions involving quasi-subordination and obtain bounds for the Fekete-Szegö functional |a3 −µa2 for the functions belonging to the above and associated classes. Some important and useful special cases of the main results are also pointed out.
Mathematics Subject Classification (2010): 30C45, 33C50, 30D60.
References
Altintas, O., Owa, S., Majorizations and quasi-subordinations for certain analytic functions, Proc. Japan Acad. Ser. A, 68(1992), no. 7, 181-185.
Cho, N.E., Kwon, O.S., Owa, S., Certain subclasses of Sakaguchi functions, Southeast Asian Bull. Math., 17(1993), 121-126.
Duren, P.L., Univalent Functions, Graduate Texts in Mathematics; 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
Fekete, M., Szego¨, G., Eine bemerkung u¨ber ungerade schlichte funktionen, J. London Math. Soc., 8(1983), 85-89.
Frasin, B.A., Coefficient inequalities for certain classes of Sakaguchi type functions, Int. J. Nonlinear Sci., 10(2010), no. 2, 206-211.
Goyal, S.P., Goswami, P., Certain coefficient inequalities for Sakaguchi type functions and applications to fractional derivative operator, Acta Univ. Apulensis Math. Inform., 19(2009), 159-166.
Goyal, S.P., Singh, O., Fekete-Szeg¨o problems and coefficient estimates of quasi subordination classes, J. Rajasthan Acad. Phys. Sci., 13(2014), no. 2, 133-142.
Keogh, F.R., Merkes, E.P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20(1969), 8-12.
Lee, S.Y., Quasi-subordinate functions and coefficient conjectures, J. Korean Math. Soc., 12(1975), no. 1, 43-50.
Littlewood, J.E., Lectures on the Theory of Functions, Oxford University Press, 1944. [11] Ma, W.C., Minda, D., A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Tianjin, 1992, Conference Proceedings Lecture Notes Analysis, International Press, Cambridge, Mass, USA, 1(1994), 157-169.
MacGregor, T.H., Majorization by univalent functions, Duke Math. J., 34(1967), 95-102. [13] Miller, S.S., Mocanu, P.T., Differential Subordinations: Theory and Applications, in: Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, 2000.
Mohd, M.H., Darus, M., Fekete-Szeg¨o problems for quasi-subordination classes, Abstr. Appl. Anal., 2012, Art. ID 192956, 14 pages.
Nehari, Z., Conformal Mapping, McGraw-Hill, New York, 1952.
Obradovic, M., A class of univalent functions, Hokkaido Math. J., 2(1988), 329-335. [17] Owa, S., Sekine, T., Yamakawa, R., Notes on Sakaguchi type functions, RIMS, Kokyuroku, 1414(2005), 76-82.
Owa, S., Sekine, T., Yamakawa, R., On Sakaguchi type functions, Appl. Math. Comput., 187(2007), 356-361.
Ravichandran, V., Darus, M., Khan, M.K., Subramanian, K.G., Fekete-Szeg¨o inequality for certain class of analytic functions, Austral. J. Math. Anal. Appl., 4(2004), no. 1, 1-7. [20] Ravichandran, V., Gangadharan, A., Darus, M., Fekete-Szeg¨o inequality for certain class of Bazilevic functions, Far East J. Math. Sci., 15(2004), 171-180.
Ren, F.Y., Owa, S., Fukui, S., Some inequalities on quasi-subordinate functions, Bull. Austral. Math. Soc., 43(1991), no. 2, 317-324.
Robertson, M.S., Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., 76(1970), 1-9.
Sakaguchi, K., On a certain univalent mapping, J. Math. Soc. Japan, 11(1959), 72-75. [24] Shanmugam, T.N., Sivasubramanian, T.N., On the Fekete-Szeg¨o problems for some subclasses of analytic functions, J. Inequal. Pure Appl. Math., 6(2005), no. 3, art. 1, 6 pages.
Sharma, P., Raina, R.K., On a Sakaguchi type class of analytic functions associated with quasi-subordination, Comment. Math. Univ. St. Pauli, 64(2015), no. 1, 59-70.
Srivastava, H.M., Mishra, A.K., Das, M.K., The Fekete-Szeg¨o problem for a subclass of close-to-convex functions, Complex Var. Theory Appl., 44(2001), 145-163.
Srivastava, H.M., Owa, S., Current Topics in Analytic Function Theory, World Scientific, Singapore, 1992.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
