Differential sandwich theorems for multivalent functions

O. Ahuja; G. Murugusundaramoorthy; S. Sivasubramanian

Annales UMCS, Mathematica (2008)

  • Volume: 62, Issue: 1, page 1-13
  • ISSN: 2083-7402

Abstract

top
In the present paper, we apply methods based on differential subordinations and superordinations in order to derive several subordination results for multivalent functions involving the Hadamard product.

How to cite

top

O. Ahuja, G. Murugusundaramoorthy, and S. Sivasubramanian. "Differential sandwich theorems for multivalent functions." Annales UMCS, Mathematica 62.1 (2008): 1-13. <http://eudml.org/doc/267636>.

@article{O2008,
abstract = {In the present paper, we apply methods based on differential subordinations and superordinations in order to derive several subordination results for multivalent functions involving the Hadamard product.},
author = {O. Ahuja, G. Murugusundaramoorthy, S. Sivasubramanian},
journal = {Annales UMCS, Mathematica},
keywords = {Analytic functions; convolution product; differential subordinations; differential superordinations; dominant; multivalent functions; subordinant; differential subordination; multivalent function; Hadamard product},
language = {eng},
number = {1},
pages = {1-13},
title = {Differential sandwich theorems for multivalent functions},
url = {http://eudml.org/doc/267636},
volume = {62},
year = {2008},
}

TY - JOUR
AU - O. Ahuja
AU - G. Murugusundaramoorthy
AU - S. Sivasubramanian
TI - Differential sandwich theorems for multivalent functions
JO - Annales UMCS, Mathematica
PY - 2008
VL - 62
IS - 1
SP - 1
EP - 13
AB - In the present paper, we apply methods based on differential subordinations and superordinations in order to derive several subordination results for multivalent functions involving the Hadamard product.
LA - eng
KW - Analytic functions; convolution product; differential subordinations; differential superordinations; dominant; multivalent functions; subordinant; differential subordination; multivalent function; Hadamard product
UR - http://eudml.org/doc/267636
ER -

References

top
  1. Ali, R. M., Ravichandran, V., Khan, M. Hussain 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. Bulboacă, T., A class of superordination-preserving integral operators, Indag. Math. (N. S.) 13 (2002), no. 3, 301-311. Zbl1019.30023
  3. Bulboacă, T., Classes of first-order differential superordinations, Demonstratio Math. 35 (2002), no. 2, 287-292. Zbl1010.30020
  4. Carlson, B. C., Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745. Zbl0567.30009
  5. Cho, N. E., Kim, T. H., Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40 (2003), no. 3, 399-410. Zbl1032.30007
  6. Cho, N. E., Srivastava, H. M., Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling 37 (2003), no. 1-2, 39-49. Zbl1050.30007
  7. Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), no. 1, 1-13.[Crossref][WoS] Zbl0937.30010
  8. Miller, S. S., Mocanu, P. T., Differential Subordinations. Theory and Applications, Marcel Dekker, New York, 2000. Zbl0954.34003
  9. Miller, S. S., Mocanu, P. T., Subordinants of differential superordinations, Complex Var. Theory Appl. 48 (2003), no. 10, 815-826. Zbl1039.30011
  10. Murugusundaramoorthy, G., Magesh, N., Differential subordinations and superordinations for analytic functions defined by the Dziok-Srivastava linear operator, J. Inequal. Pure Appl. Math. 7 (2006), no. 4, Art. 152, 9 pp. (electronic). Zbl1131.30315
  11. Obradović, M., Owa, S., On certain properties for some classes of starlike functions, J. Math. Anal. Appl. 145 (1990), no. 2, 357-364.[Crossref] Zbl0707.30009
  12. Patel, J., Cho, N. E., Some classes of analytic functions involving Noor integral operator, J. Math. Anal. Appl. 312 (2005), no. 2, 564-575.[Crossref] Zbl1082.30010
  13. Ravichandran, V., Darus, M., Khan, Hussain M. and Subramanian, K. G., Differential subordination associated with certain linear operators defined by multivalent functions, Acta Math. Vietnam. 30 (2005), no. 2, 113-121. Zbl1155.30334
  14. Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.[Crossref] Zbl0303.30006
  15. Sălăgean, G. Ş., Subclasses of univalent functions, Complex analysis - fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., 1013, Springer, Berlin, 1983, 362-372. 
  16. Shanmugam, T. N., Convolution and differential subordination, Internat. J Math. Math. Sci. 12 (1989), no. 2, 333-340.[Crossref] Zbl0683.30023
  17. 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
  18. Shanmugam, T. N., Sivasuramanian, S. and Srivastava, H. M., Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations, Integral Transforms Spec. Functions 17 (2006), no. 12, 889-899. Zbl1104.30015
  19. Shanmugam, T. N., Sivasubramanian, S. and Darus, M., On certain subclasses of functions involving a linear operator, Far East J. Math. Sci. 23 (2006), no. 3, 329-339. Zbl1211.30041
  20. Shanmugam, T. N., Sivasubramanian, S. and Owa, S., On sandwich theorems for some subclasses of analytic functions involving a linear operator, to appear in Math. Inequal. Appl. Zbl1116.30015
  21. Shanmugam, T. N., Sivasubramanian, S. and Silverman, H., On sandwich theorems for some classes of analytic functions, Int. J. Math. Math. Sci. (2006) Art. ID 29864, 13 pp. Zbl1137.30007
  22. Shenan, Gamal M., Tariq, Salim O. and Mousa, Marouf S., A certain class of multivalent prestarlike functions involving the Srivastava-Saigo-Owa fractional integral operator, Kyungpook Math. J. 44 (2004), no. 3, 353-362. Zbl1062.30018
  23. Singh, V., On some criteria for univalence and starlikeness, Indian J. Pure Appl. Math. 34 (2003), no. 4, 569-577. Zbl1114.30015
  24. Srivastava, H. M., Lashin, A. Y., Some applications of the Briot-Bouquet differential subordination, JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), no. 2, Art. 41, 7 pp. (electronic). Zbl1080.30017

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.