# Sandwich Results for Certain Subclasses of Multivalent Analytic Functions Defined by Srivastava-Attiya Operator

Aouf, M.K.;Shamandy, A.;Mostafa, A.O.;Adwan, Eman A.

• Accepted : 2011.09.23
• Published : 2012.06.23
• 16 9

#### Abstract

In this paper, we obtain some applications of first order differential subordination and superordination results involving the operator $J_{s,b}^{{\lambda},p}$ for certain normalized p-valent analytic functions associated with that operator.

#### Keywords

Multivalent functions;differential subordination;superordination;sandwich theorems;Srivastava-Attiya operator

#### References

1. R. M. Ali, V. Ravichandran and K. G. Subramanian, Differential sandwich theorems for certain analytic functions, Far East J. Math., Sci., 15(2004), 87-94.
2. M. K. Aouf , T. Bulboaca and A. O. Mostafa, Subordination properties of subclasses of p-valent functions involving certain operators, Publ. Math. Debrecen, 73(2008), 401-416.
3. T. Bulboaca, A class of superordination-preserving integral operators, Indag. Math. (N. S.)., 13(2002), 301-311. https://doi.org/10.1016/S0019-3577(02)80013-1
4. T. Bulboaca, Classes of first order differential superordinations, Demonstratio Math., 35(2002), 287-292.
5. T. Bulboaca, Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
6. J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276(2002), 432-445. https://doi.org/10.1016/S0022-247X(02)00500-0
7. V. Kumar and S. L. Shakla, Multivalent functions defined by Ruscheweyh derivatives, I, Indian J. Pure Appl. Math., 15(1984), 1216-1227
8. V. Kumar and S. L. Shakla, Multivalent functions defined by Ruscheweyh derivatives, II, Indian J. Pure Appl. Math., 15(1984), 1228-1238.
9. J. L. Liu, Subordinations for certain multivalent analytic functions associated with the generalized Srivastava-Attiya operator, Integral Transforms Spec. Funct., 18(2007), 207-216. https://doi.org/10.1080/10652460701208577
10. 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.
11. S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 28(1981), 157-171. https://doi.org/10.1307/mmj/1029002507
12. S. S. Miller and P. T. Mocanu, Subordinates of differential superordinations, Complex Variables, 48(2003), 815-826. https://doi.org/10.1080/02781070310001599322
13. J. Patel and P. Sahoo, Som applications of dierential subordination to certain oneparameter families of integral operators, Indian J. Pure Appl. Math., 35(2004), 1167-1177.
14. J. K. Prajapat and S. P. Goyal, Applications of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions, J. Math. Inequal., 3(2009), 129-137.
15. D. Raducanu and H. M. Srivastava, A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct., 18(2007), 933-943. https://doi.org/10.1080/10652460701542074
16. G. S. Salagean, Subclasses of univalent functions, Complex Analysis-Fifth Romanian-Finnish Seminar, Part 1(Bucharest, 1981), Lecture Notes in Math. (Springer-Verlag), 1013, 362-372.
17. S. Shams, S. R. Kulkarni and Jay M. Jahangiri, Subordination properties of p-valent functions defined by integral operators, Internat. J. Math. Math. Sci., (2006), Art. ID 94572, 1-3.
18. T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian, Differantial sandwich theorems for some subclasses of analytic functions, J. Austr. Math. Anal. Appl., 3(2006), Art. 8, 1-11.
19. H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transforms Spec. Funct., 18(2007), 207-216. https://doi.org/10.1080/10652460701208577
20. H. M. Srivastava and J. Choi, Series associated with the Zeta and related functions, Kluwer Academic Publishers, Dordrecht, Boston, London, 2001.
21. N. Tuneski, On certain sufficient conditions for starlikeness, Internat. J. Math. Math. Sci., 23(2000), 521-527. https://doi.org/10.1155/S0161171200003574
22. Z. G. Wang, Q. G. Li and Y. P. Jiang, Certain subclasses of multivalent analytic functions involving the generalized Srivastava-Attiya operator, Integral Transforms Spec. Funct., 21(2010), 221-234. https://doi.org/10.1080/10652460903098248