Certain properties of the Dziok–Srivastava operator Jin-Lin Liu a , H.M. Srivastava b, * a Department of Mathematics, Yangzhou University, Yangzhou 225002, Jiangsu, PR China b Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada Abstract The main object of the present paper is to investigate several interesting properties and characteristics of a linear operator H p;q;s ða 1 Þ which was recently introduced and studied in a series of papers by Dziok and Srivastava [Appl. Math. Comput. 103 (1999) 1–13; Adv. Stud. Contemp. Math. 5 (2002) 115–125; Integral Transform. Spec. Funct. 14 (2003) 7–18]. The various properties and characteristics of the linear operator H p;q;s ða 1 Þ, which are considered in this paper, are associated with (for example) the principle of differential subordination between analytic functions and a certain one- parameter family of integral operators. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Analytic functions; Hadamard product (or convolution); Differential subordination; Univalent functions; Dziok–Srivastava operator; Generalized hypergeometric functions 1. Introduction and definitions Let AðpÞ denote the class of functions of the form: f ðzÞ¼ z p þ X 1 k¼1 a pþk z pþk ðp 2 N :¼f1; 2; 3; ...gÞ; ð1:1Þ * Corresponding author. E-mail addresses: jlliucn@yahoo.com.cn (J.-L. Liu), harimsri@math.uvic.ca, hmsri@uvvm. uvic.ca (H.M. Srivastava). 0096-3003/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2003.08.133 Applied Mathematics and Computation 159 (2004) 485–493 www.elsevier.com/locate/amc