Author's personal copy A General family of integral operators and associated subordination and superordination properties of some special analytic function classes Nak Eun Cho a , Teodor Bulboaca ˘ b , H.M. Srivastava c,⇑ a Department of Applied Mathematics, Pukyong National University, Pusan 608-737, Republic of Korea b Faculty of Mathematics and Computer Science, Babes ß-Bolyai University, R-400084 Cluj-Napoca, Romania c Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada article info Keywords: Integral operators Differential subordination Differential superordination Sandwich-type results Univalent functions Starlike and convex functions Close-to-convex functions Subordination (or Löwner) chains abstract In the present paper, we obtain the subordination- and superordination-preserving prop- erties of a certain general family of nonlinear integral operators which are defined on the space of normalized analytic functions in the open unit disk. The sandwich-type results for these integral operators are also presented. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction, definitions and preliminaries Let H ¼ HðUÞ denote the class of analytic functions in the open unit disk U ¼fz : z 2 C and jzj < 1g: For a 2 C and n 2 N ¼f1; 2; 3; ...g, let H½a; n¼ff : f 2 H and f ðzÞ¼ a þ a n z n þ a nþ1 z nþ1 þ   g: Let the functions f and F be in the class H. The function f is said to be subordinate to F or, equivalently, the function F is said to be superordinate to f, if there exists a Schwarz function w analytic in U, with wð0Þ¼ 0 and jwðzÞj < 1 ðz 2 UÞ; such that f ðzÞ¼ F  wðzÞ  ðz 2 UÞ: In such a case, we write f  F or f ðzÞ F ðzÞ ðz 2 UÞ: Furthermore, if the function F is univalent in U, then we have (cf. [13]) f  F () f ð0Þ¼ F ð0Þ and f ðUÞ F ðUÞ: 0096-3003/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.amc.2012.08.075 ⇑ Corresponding author. E-mail addresses: necho@pknu.ac.kr (N.E. Cho), bulboaca@math.ubbcluj.ro (T. Bulboaca ˘), harimsri@math.uvic.ca (H.M. Srivastava). Applied Mathematics and Computation 219 (2012) 2278–2288 Contents lists available at SciVerse ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc