• Aouf, Mohamed K. ;
  • Seoudy, Tamer M.
  • Received : 2009.10.22
  • Published : 2011.05.31


In this paper, we obtain some applications of first order differential subordination and superordination results for higher-order derivatives of p-valent functions involving certain linear operator. Some of our results improve and generalize previously known results.


analytic function;Hadamard product;differential subordination;superordination;linear operator


  1. R. M. Ali, V. Ravichandran, M. H. Khan, and K. G. Subramanian, Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci. (FJMS) 15 (2004), no. 1, 87-94.
  2. M. K. Aouf, Generalization of certain subclasses of multivalent functions with negative coefficients defined by using a differential operator, Math. Comput. Modelling 50 (2009), no. 9-10, 1367-1378.
  3. M. K. Aouf , On certain multivalent functions with negative coefficients de ned by using a differential operator, Indian J. Math. 51 (2009), no. 2, 433-451.
  4. M. K. Aouf and A. O. Mostafa, On a subclass of n-p-valent prestarlike functions, Comput. Math. Appl. 55 (2008), no. 4, 851-861.
  5. T. Bulboaca, Classes of first-order differential superordinations, Demonstratio Math. 35 (2002), no. 2, 287-292.
  6. T. Bulboaca, Differential Subordinations and Superordinations, Recent Results, House of Science Book Publ. Cluj-Napoca, 2005.
  7. B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), no. 4, 737-745.
  8. M. Kamali and H. Orhan, On a subclass of certain starlike functions with negative coefficients, Bull. Korean Math. Soc. 41 (2004), no. 1, 53-71.
  9. S. S. Miller and P. T. Mocanu, Differential Subordination, Monographs and Textbooks in Pure and Applied Mathematics, 225. Marcel Dekker, Inc., New York, 2000.
  10. S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Var. Theory Appl. 48 (2003), no. 10, 815-826.
  11. V. O. Nechita, Differential subordinations and superordinations for analytic functions defined by the generalized Salagean derivative, Acta Univ. Apulensis Math. Inform. No. 16 (2008), 143-156.
  12. S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.
  13. G. S. Salagean, Subclasses of univalent functions, Complex analysis - fifth Romanian- Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin, 1983.
  14. T. N. Shanmugam, V. Ravichandran, and S. Sivasubramanian, Differantial sandwich theorems for some subclasses of analytic functions, J. Austr.Math. Anal. Appl. 3 (2006), no. 1, Art. 8, 1-11.
  15. N. Tuneski, On certain sufficient conditions for starlikeness, Int. J. Math. Math. Sci. 23 (2000), no. 8, 521-527.

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