# Differential Subordinations and Superordinations of Certain Meromorphic Functions associated with an Integral Operator

• DARWISH, HANAN ELSAYED (Department of Mathematics, Faculty of Science, Mansoura University) ;
• LASHIN, ABD AL-MONEM YOUSOF (Department of Mathematics, Faculty of Science, Mansoura University) ;
• SOILEH, SOLIMAN MOHAMMED (Department of Mathematics, Faculty of Science, Mansoura University)
• Accepted : 2014.04.22
• Published : 2015.09.23
• 36 21

#### Abstract

Differential subordinations and superordinations results are obtained for certain meromorphic functions in the punctured unit disk which are associated with an integral operator. These results are obtained by investigating appropriate classes of a dmissible functions. Sandwich-type results are also obtained.

#### References

1. R. Aghalary, R. M. Ali, S. B. Joshi and V. Ravichandran, Inequalities for analytic functions defined by certain linear operator, Internat. J. Math. Sci., 4(2)(2005), 267-274.
2. R. M. Ali, V. Ravichandran and N. Seenivasagan, Differential Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions, Bull. Malaysian Math. Sci. Soc., 31(2)(2008), 193-207.
3. R. M. Ali, V. Ravichandran and N. Seenivasagan, Differential subordination and superordination of analytic functions defined by the multiplier transformation, Math. Inequal. Appl., 12(1)(2009), 123-139.
4. M. K . Aouf, Inequalities involving certain intergral operators, J. Math. Inequal., 2(2)(2008), 537-547.
5. M. K. Aouf , H. M. Hossen and A. Y. Lashin, An application of certain integral operators, J. Math. Anal. Appl., 248(2)(2000), 475-481. https://doi.org/10.1006/jmaa.2000.6923
6. M. K. Aouf and T. M. Seoudy, Differential subordination and superordintion of analytic functions defined by the integral operator, Euro. J. Pure Appl. Math., 3(1)(2010), 26-44.
7. I. B. Jung, Y. C. kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one- parameter families of integral operators, J. Math. Anal. Appl., 176(1)(1993), 138-147. https://doi.org/10.1006/jmaa.1993.1204
8. M. Kamali, On certain meromorphic p-valent starlike functions, J. Franklin Institute, 344(6)(2007), 867-872. https://doi.org/10.1016/j.jfranklin.2006.11.003
9. Y. C. Kim and H. M. Srivastava, Inequalities involving certain families of integral and convoluion operators, Math. Inequal. Appl., 7(2)(2004), 227-234.
10. A. Y. Lashin, On certain subclases of meromorphic functions associated with certain integral operators, Comput. Math. Appl., 59(2009), 524-531.
11. J. Liu and S. Owa, On certain meromorphic p-valent functions, Taiwanese J. Math., 2(1)(1998), 107-110.
12. S. S. Miller and P. T. Mocanu, Differential subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied mathemetics, Vol. 225, Marcel Dekker Inc., New York and Basel, 2000.
13. S. S. Miller and P. T. Mocanu, Subordinates of differential superordintions, Complex variables, Theory Appl., 48(10)(2003), 815-826.