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Differential Sandwich Theorems of Analytic Functions Defined by Linear Operators

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Abstract (2. Language): 
In this paper, we obtain some applications of first order differential subordination and superordination results involving a linear operator and other linear operators for certain normalized analytic functions. Some of our results generalize previously known results.
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REFERENCES

References: 

[1] R. M. Ali, V. Ravichandran, and K. G. Subramanian. Differential sandwich theorems for
certain analytic functions. Far East J. Math. Sci., 15(1):87–94, 2004.
[2] F. M. AlOboudi. On univalent functions defined by a generalized Salagean operator.
Internat. J. Math. Math. Sci., 27:1429–1436, 2004.
[3] M. K. Aouf and T. M. Seoudy. On differential sandwich theorems of analytic functions
defined by certain linear operator. Ann. Univ. Mariae Curie-Sklodowska Sect. A, (To
appear).
[4] S. D. Bernardi. Convex and starlike univalent functions. Trans. Amer. Math. Soc.,
135:429–446, 1969.
[5] T. Bulboaca. Classes of first order differential superordinations. Demonstratio Math.,
35(2):287–297, 2002.
[6] T. Bulboaca. Differential Subordinations and Superordinations, Recent Results. House of
Scientific Book Publ., Cluj-Napoca, 2005.
[7] B. C. Carlson and D. B. Shaffer. Starlike and prestarlike hypergeometric functions. SIAM
J. Math. Anal., 15:737–745, 1984.
[8] A. Catas, G. I. Oros, and G. Oros. Differential subordinations associated with multiplier
transformations. Abstract Appl. Anal., 2008,ID 845724:1–11, 2008.
[9] N. E. Cho and T. G. Kim. Multiplier transformations and strongly close-to-convex functions.
Bull. Korean Math. Soc., 40(3):399–410, 2003.
[10] J. Dziok and H. M. Srivastava. Classes of analytic functions associated with thegeneralized
hypergeometric function. Appl. Math. Comput., 103:1–13, 1999.
[11] J. Dziok and H. M. Srivastava. Some subclasses of analytic functions with fixed argument
of coefficients associated with the generalized hypergeometric function. Adv. Stud.
Contemp. Math., 5:115–125, 2002.
[12] J. Dziok and H. M. Srivastava. Certain subclasses of analytic functions associated with
the generalized hypergeometric function. Integral Transform. Spec. Funct., 14:7–18,
2003.
[13] Yu. E. Hohlov. Operators and operations in the univalent functions. Izv. Vysˆsh. Uˇcebn.
Zaved. Mat.( in Russian), 10:83–89, 1978.
[14] R. J. Libera. Some classes of regular univalent functions. Proc. Amer. Math. Soc., 16:755–
658, 1965.
[15] A. E. Livingston. On the radius of univalence of certain analytic functions. Proc. Amer.
Math. Soc., 17:352–357, 1966.
[16] S. S. Miller and P. T. Mocanu. Differential Subordination: Theory and Applications, Series
on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225. Marcel Dekker
Inc., New York and Basel, 2000.
[17] S. S. Miller and P. T. Mocanu. Subordinates of differential superordinations. Complex
Variables, 48(10):815–826, 2003.
[18] V. O. Nechita. Differential subordinations and superordinations for analytic functions
defined by the generalized S˘al˘agean derivative. Acta Univ. Apulensis, 16:143–156, 2008.
[19] S. Owa and H. M. Srivastava. Univalent and starlike generalized hypergeometric functions.
Canad. J. Math., 39:1057–1077, 1987.
[20] St. Ruscheweyh. New criteria for univalent functions. Proc. Amer. Math. Sco., 49:109–
115, 1975.
[21] H. Saitoh. A linear operator ana its applications of fiest order differential subordinations.
Math. Japon., 44:31–38, 1996.
[22] G. S. Salagean. Subclasses of univalent functions. Lecture Notes in Math. (Springer-
Verlag), 1013:362–372, 1983.
[23] C. Selvaraj and K. R. Karthikeyan. Differential subordination and superordination for
certain subclasses of analytic functions. Far East J. Math. Sci., 29(2):419–430, 2008.
[24] T. N. Shanmugam, V. Ravichandran, and S. Sivasubramanian. Differantial sandwich
theorems for some subclasses of analytic functions. J. Austr. Math. Anal. Appl., 3(1, Art.
8):1–11, 2006.
[25] N. Tuneski. On certain sufficient conditions for starlikeness. Internat. J. Math. Math.
Sci., 23(8):521–527, 2000.

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