Differential Sandwich Theorems for Analytic Functions Defined by an Extended Multiplier Transformation

Amnah Shammaky

Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia.

DOI: 10.4236/apm.2012.25045                

Abstract

In this investigation, we obtain some applications of first order differential subordination and superordination results involving an extended multiplier transformation and other linear operators for certain normalized analytic functions. Some of our results improve previous results.

Keywords

Differential Sandwich Theorems; Analytic Functions; Multiplier Transformation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. Bulboaca, “Differential Superordinations and Superordinations,” Recent Results, House of Scientific, Cluj-Napoca.
[2]	S. S. Miller and P. T. Mocanu, “Differential Subordinations and Univalent Functions,” Michigan Math Journal, Vol. 28, No. 2, 1981, pp. 157-171.doi:10.1307/mmj/1029002507
[3]	S. S. Miller and P. T. Mocanu, “Differential Subordinations: Theory and Applications,” Pure and Applied Mathematics No. 225, Marcel Dekker, New York, 2000.
[4]	S. S. Miller and P. T. Mocanu, “Subordinants of Differential Superordinations,” Complex Variables, Vol. 48, No. 10, 2003, pp. 815-826. doi:10.1080/02781070310001599322
[5]	T. Bulboaca, “Classes of First-Order Differential Superordinations,” Demonstratio Mathematica, Vol. 35, No. 2, 2002, pp. 287-292.
[6]	T. Bulboaca, “A Class of Superordination-Preserving Integral Operators,” Indagationes Mathematicae, Vol. 13, No. 3, 2002, pp. 301-311. doi:10.1016/S0019-3577(02)80013-1
[7]	R. M. Ali, V. Ravichandran, M. Hussain Khan and K. G. Subramanian, “Differential Sandwich Theorems for Certain Analytic Functions,” Far East Journal of Mathematical Sciences, Vol. 15, No. 1, 2005, pp. 87-94
[8]	N. Tuneski, “On Certain Sufficient Conditions for Starlikeness,” International Journal of Mathematics and Mathematical Sciences, Vol. 23, No. 8, 2000, pp. 521-527. doi:10.1155/S0161171200003574
[9]	T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian, “Differential Sandwich Theorems for Some Subclasses of Analytic Functions,” Australian Journal of Mathematical Analysis and Applications, Vol. 3, No. 1, 2006, Article 8, 11.
[10]	N. E. Cho and H. M. Srivastava, “Argument Estimates of Certain Analytic Functions Defined by a Class of Multiplier Transformations,” Mathematical and Computer Modelling, Vol. 37, No. 1-2, 2003, 39-49. doi:10.1016/S0895-7177(03)80004-3
[11]	N. E. Cha and T. H. Kim, “Multiplier Tnsformations and Strongly Close-to-Convex Functions,” Bulletin of the Korean Mathematical Society, Vol. 40, No. 3, 2003, 399-410. doi:10.4134/BKMS.2003.40.3.399
[12]	B. A. Uralegaddi and C. Somanama, “Certain Classes of Univalent Functions,” In: H. M. Srivastava and S. Owa, Eds., Current Topics in Analytic Function Theory, World Scientific, Publishing Company, Singapore City, 1992, pp. 371-374.
[13]	A. Catas, “A Note on a Certain Subclass of Analytic Functions Defined by Multiplier Transformations,” Proceedings of the Internat, Symposium on Geometric Function Theory and Applications, Istanbul, 20-24 August 2007.
[14]	F. M. Al-Oboudi, “On Univalent Functions de Fined by a Generalized Salagean Operator Internat,” International Journal of Mathematics and Mathematical Sciences, Vol. 27, 2004, pp. 1429-1436. doi:10.1155/S0161171204108090
[15]	G. S. Salagean, “Subclasses of Univalent Functions,” Lecture Notes in Mathematics, Vol. 1013, 1983, pp. 362-372. doi:10.1007/BFb0066543