On sandwich theorems for some subclasses defined by generalized hypergeometric functions
DOI:
https://doi.org/10.24193/subbmath.2017.0007Keywords:
Differential subordination, superordination, hypergeometric function.Abstract
In this paper we derive some subordination and superordination results for certain normalized analytic functions in the open unit disc, which are acted upon by a class of generalized hypergeometric function Hq,s(α1).
Mathematics Subject Classification (2010): 30C45, 30C80.
References
Ali, R.M., Ravichandran, V., Khan, M.H., Subramaniam, K.G., Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci., 15(2004), no. 1, 87-94.
Aouf, M.K., Al-Oboudi, F.M., Haidan, M.M., On some results for λ-spirallike and λ- Robertson functions of complex order, Publ. Institute Math. Belgrade, 77(2005), no. 91, 93-98.
Bernardi, S.D., Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135(1969), 429-446.
Bulboaca˘, T., A class of superordination preserving integral operators, Indag. Math. (New Series), 13(2002), no. 3, 301-311.
Bulboaca˘, T., Classes of first-order differential subordinations, Demonstratio Math., 35(2002), no. 2, 287-392.
Carlson, B.C., Shaffer, D.B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15(1984), 737-745.
Cho, N.E., Kwon, O.H., Srivastava, H.M., Inclusion and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292(2004), 470-483.
Choi, J.H., Saigo, M., Srivastava, H.M., Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276(2002), 432-445.
Dziok, J., Srivastava, H.M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103(1999), 1-13.
Dziok, J., Srivastava, H.M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct., 14(2003), 7-18.
Hallenbeck, D.J., Ruscheweyh, St., Subordination by convex functions, Proc. Amer. Math. Soc., 52(1975), 191-195.
Hohlov, Yu.E., Operators and operations in the class of univalent functions, (in Russian), Izv. Vys˘sh. U˘cebn. Zaved. Mat., 10(1978), 83-89.
Libera, R.J., Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16(1965), 755-658.
Livingston, A.E., On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc., 17(1966), 352-357.
Miller, S.S., Mocanu, P.T., Differential subordinations and univalent functions, Michigan Math. J., 28(1981), 157-171.
Miller, S.S., Mocanu, P.T., Differential Subordinations Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Math., No. 225, Marcel Dekker Inc. New York, Basel, 2000.
Miller, S.S., Mocanu, P.T., Subordinations of differential superordinations, Complex Variables, 48(2003), no. 10, 815-826.
Noor, K.I., On new classes of integral operator, J. Nat. Geom., 16(1999), no. 1-2, 71-80. [19] Obradovic, M., Aouf, M.K., Owa, S., On some results for starlike functions of complex order, Publ. Inst. Math. Belgrade, 46(1989), no. 60, 79-85.
Obradovic, M., Owa, S., On certain properties for some classes of starlike functions, J. Math. Anal. Appl., 145(1990), no. 2, 357-364.
Owa, S., Srivastava, H.M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39(1987), 1057-1077.
Ruscheweyh, St., New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109-115.
Shanmugam, T.N., Ravichandran, V., Sivasubramanian, S., Differential sandwich theorems for some subclasses of analyitc functions, Austral. J. Math. Anal. Appl., 3(2006), no. 1, 1-11.
Shanmugam, T.N., Sivasubramanian, S., Owa, S., On sandwich results for some subclasses of analytic functions involving certain linear operator, Integral Transform. Spec. Funct., 21(2010), no. 1, 1-11.
Srivastava, H.M., Karlsson, P.W., Multiple Gaussian Hypergeometric Series, Ellis Horwood Ltd., Chichester, Halsted Press (John Wiley & Sons, Inc.), New York, 1985.
Srivastava, H.M., Lashin, A.Y., Some applications of the Briot-Bouquet differential subordination, J. Inequal. Pure Appl. Math., 6(2005), no. 2, 1-7.
Tuneski, N., On certain sufficient conditions for starlikeness, Internat. J. Math. Math. Sci., 23(2000), no. 8, 521-527.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
