Preserving subordination and superordination results of generalized Srivastava-Attiya operator

In this paper, we obtain some subordination and superordination-preserving results of the generalized Srivastava-Attyia operator. Sandwichtype result is also obtained.

Full text (pdf)

1. J.W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. Math. Ser., 2, 17 (1915), 12-22.
2. M. K. Aouf and T. M. Seoudy, Some preserving subordination and superordination results of certain integral operator, Int. J. Open Problems Comput. Math., (to appear).
3. J. H. Choi and H. M. Srivastava, Certain families of series associated with the Hurwitz-Lerch Zeta function, Appl. Math. Comput., 170 (2005), 399-409.
4. 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.
5. R. M. El-Ashwah and M. K. Aouf, Some properties of new integral operator, Acta Univ. Apulensis, 24 (2010), 51-61.
6. T. 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 (1993), 138-147.
7. R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16 (1969), 755-758.
8. S.-D. Lin and H. M. Srivastava, Some families of the Hurwitz-Lerch Zeta functions and  associated fractional derivative and other integral representations, Appl. Math. Comput., 154 (2004), 725-733.
9. S.-D. Lin, H. M. Srivastava and P.-Y. Wang, Some expansion formulas for a class of eneralized Hurwitz-Lerch Zeta functions, Integral Transforms Spec. Funct., 17 (2006), 17-827.
10. J.-L. Liu, Subordinations for certain multivalent analytic functions associated with the generalized Srivastava-Attiya operator, Integral Transforms Spec. Funct., 18 (2007), 207-216.
11. Q.-M. Luo and H. M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. Appl., 308 (2005), 290-302.
12. S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 28 (1981), no. 2, 157–172.
13. S. S. Miller and P. T. Mocanu, Univalent solutions of Briot-Bouquet differential equations,  J. Differential Equations, 56 (1985), no. 3, 297–309. 
14. S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York and Basel, 2000.
15. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex
    Variables. Theory Appl., 48 (2003), no. 10, 815–826.
16. Ch. Pommerenke, Univalent Functions, Vandenhoeck and Ruprecht, G¨ottingen, 1975.
17. S. Shams, S. R. Kulkarni, and J. M. Jahangiri, Subordination properties of p–valent
    functions defined by integral operators, Internat. J. Math. Math. Sci., Vol. 2006, Art. ID
    94572, 1–3.
18. H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hur witz-Lerch Zeta function and differential subordination, Integral Transforms Spec. Funct., 18 (2007), 207-216.
19. H. M. Srivastava and J. Choi, Series associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, London, 2001.