Subordinations for analytic functions defined by the Dziok–Srivastava linear operator R. Aghalary a, * , S.B. Joshi b , R.N. Mohapatra c , V. Ravichandran d a Department of Mathematics, University of Urmia, Urmia, Iran b Department of Mathematics, Walchand College of Engineering, Sangli 416415, Maharashtra, India c Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA d School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia Dedicated to Professor H.M. Srivastava on the occasion of his 65th birthday Abstract In the present investigation, we obtain certain sufficient conditions for a normalized analytic function f(z) defined by the Dziok–Srivastava linear operator H l m ½a 1  to satisfy the certain subordination. Our results extend corresponding previously known results on starlikeness, convexity, and close to convexity. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Univalent functions; Starlike functions; Convex functions; Differential subordination; Convolution; Dziok–Srivastava linear operator 1. Introduction Let H denote the class of analytic functions defined on the open unit disc D ¼fz 2 C :j z j< 1g. Let A denote the subclass of H consisting of functions f(z) normalized by f(0) = f 0 (0)  1 = 0. For the functions f and g in H, we say that f is subordinate to g in D, and write f  g, if there exists a Schwarz function x in H with jx(z)j < 1 and x(0) = 0 such that f(z)= g(x(z)) in D. For two functions f ðzÞ¼ z þ P 1 k¼2 a k z k and gðzÞ¼ z þ P 1 k¼2 b k z k , the Hadamard product (or convolution) of f and g is defined by ðf  gÞðzÞ :¼ z þ X 1 k¼2 a k b k z k ¼: ðg  f ÞðzÞ: 0096-3003/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2006.08.097 * Corresponding author. E-mail addresses: raghalary@yahoo.com (R. Aghalary), joshisb@hotmail.com (S.B. Joshi), ramm@mail.ucf.edu (R.N. Mohapatra), vravi@cs.usm.my (V. Ravichandran). URL: http://cs.usm.my/~vravi (V. Ravichandran). Applied Mathematics and Computation 187 (2007) 13–19 www.elsevier.com/locate/amc