On differential sandwich theorems of analytic functions defined by certain linear operator

Mohamed K. Aouf, Tamer M. Seoudy

Abstract


In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results.

Keywords


Analytic function; Hadamard product; differential subordination; superordination; linear operator

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References


Ali, R. M., Ravichandran, V. and Subramanian, K. G., Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci., 15(1) (2004), 87-94.

Al-Oboudi, F., On univalent functions defined by a generalized Salagean operator, Internat. J. Math. Math. Sci. 27 (2004), 1429-1436.

Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446.

Bulboaca, T., Classes of first order differential superordinations, Demonstratio Math. 35(2) (2002), 287-292.

Bulboaca, T., Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.

Carlson, B. C., Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745.

Cata¸s, A., Oros, G. I. and Oros, G., Differential subordinations associated with multiplier transformations, Abstr. Appl. Anal. 2008 (2008), Art. ID 845724, 1-11.

Cho, N. E., Kim, T. G., Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40(3) (2003), 399-410.

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., Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function, Adv. Stud. Contemp. Math. (Kyungshang) 5 (2002), 115-125.

Dziok, J., Srivastava, H. M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct. 14 (2003), 7-18.

Hohlov, Yu. E., Operators and operations on the class of univalent functions, Izv. Vyssh. Uchebn. Zaved. Mat. 10 (1978), 83-89 (Russian).

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 Subordination: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York, Basel, 2000.

Miller, S. S., Mocanu, P. T., Subordinates of differential superordinations, Complex Var. Theory Appl. 48(10) (2003), 815-826.

Nechita, V. O., Differential subordinations and superordinations for analytic functions defined by the generalized S˘al˘agean derivative, Acta Univ. Apulensis 16 (2008), 143-156.

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.

Saitoh, H., A linear operator and its applications of first order differential subordinations, Math. Japon. 44 (1996), 31-38.

Salagean, G. S., Subclasses of univalent functions, Complex analysis - fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math. 1013, Springer-Verlag, Berlin, 1983.

Selvaraj, C., Karthikeyan, K. R., Differential subordination and superordination for certain subclasses of analytic functions, Far East J. Math. Sci. (FJMS) 29(2) (2008), 419-430.

Shanmugam, T. N., Ravichandran, V. and Sivasubramanian, S., Differential sandwich theorems for some subclasses of analytic functions, Aust. J. Math. Anal. Appl. 3(1) (2006), Art. 8, 1-11.

Tuneski, N., On certain sufficient conditions for starlikeness, Internat. J. Math. Math. Sci. 23(8) (2000), 521-527.




DOI: http://dx.doi.org/10.2478/v10062-010-0009-7
Date of publication: 2016-07-29 10:39:53
Date of submission: 2016-07-28 18:31:37


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