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Certain properties of the Dziok--Srivastava operator. (English) Zbl 1081.30021
Making use of Hadamard product (or convolution), a certain linear operator $H_{p,q,s}(\alpha _1)$ was recently introduced and studied in a series of papers by Dziok and Srivastava. In this paper, some other properties of the operator $H_{p,q,s}(\alpha _1)$ are derived with the help of differential subordination.

30C45Special classes of univalent and multivalent functions
30C50Coefficient problems for univalent and multivalent functions
Full Text: DOI
[1] Dziok, J.; Srivastava, H. M.: Classes of analytic functions associated with the generalized hypergeometric function. Appl. math. Comput 103, 1-13 (1999) · Zbl 0937.30010
[2] Dziok, J.; Srivastava, H. M.: Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function. Adv. stud. Contemp. math 5, 115-125 (2002) · Zbl 1038.30009
[3] Dziok, J.; Srivastava, H. M.: Certain subclasses of analytic functions associated with the generalized hypergeometric function. Integral transform. Spec. funct 14, 7-18 (2003) · Zbl 1040.30003
[4] Gangadharan, A.; Shanmugam, T. N.; Srivastava, H. M.: Generalized hypergeometric functions associated with k-uniformly convex functions. Comput. math. Appl 44, 1515-1526 (2002) · Zbl 1036.33003
[5] Kim, Y. C.; Srivastava, H. M.: Fractional integral and other linear operators associated with the Gaussian hypergeometric function. Complex variables theory appl 34, 293-312 (1997) · Zbl 0951.30010
[6] Liu, J. -L.: Strongly starlike functions associated with the dziok--Srivastava operator. Tamkang J. Math 35 (2004) · Zbl 1064.30006
[7] Liu, J. -L.; Srivastava, H. M.: Classes of meromorphically multivalent functions associated with the generalized hypergeometric function. Math. comput. Modelling 38 (2004) · Zbl 1049.30008
[8] Miller, S. S.; Mocanu, P. T.: Differential subordinations and univalent functions. Michigan math. J 28, 157-171 (1981) · Zbl 0439.30015
[9] S.S. Miller, P.T. Mocanu, Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York, 2000
[10] Owa, S.; Srivastava, H. M.: Univalent and starlike generalized hypergeometric functions. Canad. J. Math 39, 1057-1077 (1987) · Zbl 0611.33007
[11] Srivastava, H. M.; Owa, S.: Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions. Nagoya math. J 106, 1-28 (1987) · Zbl 0607.30014
[12] Srivastava, H. M.; Owa, S.: Univalent functions, fractional calculus, and their applications. (1989) · Zbl 0683.00012
[13] Srivastava, H. M.; Owa, S.: Current topics in analytic function theory. (1992) · Zbl 0976.00007