Journal of Mathematics and Applications
06/36, DOI: 10.7862/rf.2013.6
Convolution properties of subclasses of analytic functions associated with the Dziok-Srivastava operator
S. P. Goyal, Sanjay Kumar Bansal, Pranay Goswami, Zhi-Gang Wang
DOI: 10.7862/rf.2013.6
Abstract
The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the Dziok-Srivastava operator. We further investigate convolution properties for these calsses. We also nd necessary and sucient condition and coecient estimate for them.
References
- Ahuja, O.P, Families of analytic functions related to Ruscheweyh derivatives and subordinate to convex functions, Yokohama Math. J. 41 (1993), 39-50.
- Aouf, M.K and Seoudy, T.M., Calsses of analytic functions related to the Dziok-Srivastav operator, Integral Transform and Special Function 1 (2010), 1-8.
- Carlson, B.C. and Sha er, D.B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745.
- Dziok, J. and Srivastava, H.M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003), 7-18.
- Dziok, J., Inclusion relationships between classes of functions de ned by subordination. Ann. Polon. Math. 100 (2011), no. 2, 193-202.
- Hohlov, Yu.E., Operators and operations in the class of univalent functions, Izv. Vyssh. Uchebn. Zaved. Mat. 10 (1978), 83-89 (in Russian).
- Murugusundaramoorthy, G. and Magesh, N., Starlike and convex functions of complex order involving the Dziok-Srivastava operator, Integral Transforms Spec. Funct. 18(6) (2007), 419-425.
- Noor, K.I., On new classes of integral operator, J. Nat. Geom. 16(1-2) (1999), 71-80.
- Ruscheweyh, St., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.
- Silverman, H. and Silvia, E.M., Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 1 (1985), 48-61.
- Silverman, H., Silvia, E.M. and Telage, D., Convolution conditions for convexity, starlikeness and spiral-likeness, Math. Z 162 (1978), 125-130.
- Srivastava, H. M. and Karlsson, P.W., Multiple Gaussian Hypergeometric Series, Ellis Horwood, Ltd., Chichester, Halsted Press, John-Wiley and Sons, Inc.,NewYork, 1985.
- Srivastava, H.M., Murugusundaramoorthy, G. and Sivasubramanian, S., Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integral Transforms Spec. Funct. 18(7) (2007), 511-520.
- Srivastava, H.M., Yang, D.G. and Xu, N. E., Subordinations for multivalent analytic functions associated with the Dziok-Srivastava operator, Integral Transforms Spec. Funct. 20(8) (2009), 581-606.
- Wang, Z.G., Jiang, Y. P., and Srivastava, H.M., Some subclasses of multivalent analytic functions involving the Dziok-Srivastava operator, Integral Transforms Spec. Funct. 19(2) (2008), 29-146.
About this Article
TITLE:
Convolution properties of subclasses of analytic functions associated with the Dziok-Srivastava operator
AUTHORS:
S. P. Goyal (1)
Sanjay Kumar Bansal (2)
Pranay Goswami (3)
Zhi-Gang Wang (4)
AUTHORS AFFILIATIONS:
(1) Department of Mathematics, University of Rajasthan, Jaipur-302055, India
(2) Department of Mathematics, Bansal School of Engg. and Tech., Jaipur-303904, India
(3) Department of Mathematics School of Liberal Studies, Bharat Ratna Dr B.R. Ambed-
kar University, Delhi-110006, India
(4) School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 410076, Hunan, Peoples Republic of China
JOURNAL:
Journal of Mathematics and Applications
06/36
KEY WORDS AND PHRASES:
analyitc function; Hadmard product; starlike function; convex function; subordination and Dziok-Srivastava operator
FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/14
DOI:
10.7862/rf.2013.6
URL:
http://dx.doi.org/10.7862/rf.2013.6
RECEIVED:
2012-06-22
ACCEPTED:
2013-10-31
COPYRIGHT:
Publishing House of Rzeszow University of Technology Powstańców Warszawy 12, 35-959 Rzeszow