Differential sandwich theorems for analytic functions defined by some linear operators

M. Aouf; A. Mostafa; R. El-Ashwah

Annales UMCS, Mathematica (2008)

  • Volume: 62, Issue: 1, page 15-29
  • ISSN: 2083-7402

Abstract

top
In this investigation, we obtain some applications of first order differential subordination and superordination results involving Dziok-Srivastava operator and other linear operators for certain normalized analytic functions. Some of our results improve previous results.

How to cite

top

M. Aouf, A. Mostafa, and R. El-Ashwah. "Differential sandwich theorems for analytic functions defined by some linear operators." Annales UMCS, Mathematica 62.1 (2008): 15-29. <http://eudml.org/doc/268277>.

@article{M2008,
abstract = {In this investigation, we obtain some applications of first order differential subordination and superordination results involving Dziok-Srivastava operator and other linear operators for certain normalized analytic functions. Some of our results improve previous results.},
author = {M. Aouf, A. Mostafa, R. El-Ashwah},
journal = {Annales UMCS, Mathematica},
keywords = {Analytic functions; differential subordination; superordination; sandwich theorems; Dziok-Srivastava operator},
language = {eng},
number = {1},
pages = {15-29},
title = {Differential sandwich theorems for analytic functions defined by some linear operators},
url = {http://eudml.org/doc/268277},
volume = {62},
year = {2008},
}

TY - JOUR
AU - M. Aouf
AU - A. Mostafa
AU - R. El-Ashwah
TI - Differential sandwich theorems for analytic functions defined by some linear operators
JO - Annales UMCS, Mathematica
PY - 2008
VL - 62
IS - 1
SP - 15
EP - 29
AB - In this investigation, we obtain some applications of first order differential subordination and superordination results involving Dziok-Srivastava operator and other linear operators for certain normalized analytic functions. Some of our results improve previous results.
LA - eng
KW - Analytic functions; differential subordination; superordination; sandwich theorems; Dziok-Srivastava operator
UR - http://eudml.org/doc/268277
ER -

References

top
  1. Ali, R. M., Ravichandran, V. and Subramanian, K. G., Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci. 15 (2004), no. 1, 87-94. Zbl1074.30022
  2. Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. Zbl0172.09703
  3. Bulboacă, T., Classes of first order differential superordinations, Demonstratio Math. 35 (2002), no. 2, 287-292. Zbl1010.30020
  4. Bulboacă, T., Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005. 
  5. Bulboacă, T., A class of superordination-preserving integral operators, Indag. Math. (N. S.) 13 (2002), no. 3, 301-311.[Crossref] Zbl1019.30023
  6. Carlson, B. C. and Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745.[Crossref] Zbl0567.30009
  7. Cho, N. E., Kwon, O. H. and Srivastava, H. M., Inclusion and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004), 470-483. Zbl1059.30006
  8. Choi, J. H., Saigo, M. and Srivastava, H. M., Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002), 432-445. Zbl1035.30004
  9. Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13.[Crossref][WoS] Zbl0937.30010
  10. Dziok, J., Srivastava, H. M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct. 14 (2003), 7-18.[Crossref] Zbl1040.30003
  11. Libera, R. J., Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965), 755-658.[Crossref] Zbl0158.07702
  12. Miller, S. S., Mocanu, P. T., Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), no. 2, 157-171. Zbl0439.30015
  13. Miller, S. S., Mocanu, P. T., Differential Subordination. Theory and Applications, Marcel Dekker Inc., New York, 2000. 
  14. Miller, S. S., Mocanu, P. T., Subordinates of differential superordinations, Complex Variables 48 (2003), no. 10, 815-826. Zbl1039.30011
  15. Ruscheweyh, St., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.[Crossref] Zbl0303.30006
  16. Shanmugam, T. N., Ravichandran, V. and Sivasubramanian, S., Differential sandwich theorems for some subclasses of analytic functions, Aust. J. Math. Anal. Appl. 3 (2006), no. 1, Art. 8, 11 pp. (electronic). Zbl1091.30019
  17. Srivastava, H. M., Karlsson, P. W., Multiple Gaussian Hypergeometric Series, Ellis Horwood Ltd., Chichester, Halsted Press (John Wiley & Sons, Inc.), New York, 1985. Zbl0552.33001
  18. Tuneski, N., On certain sufficient conditions for starlikeness, Int. J. Math. Math. Sci. 23 (2000), no. 8, 521-527.[Crossref] Zbl0954.30003

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.