KYUNGPOOK Math. J. 54(2014), 453-461 http://dx.doi.org/10.5666/KMJ.2014.54.3.453 Certain Class of Analytic Functions Defined by Ruscheweyh Derivative with Varying Arguments Rabha Mohamed El-Ashwah Department of Mathematics, Faculty of Science, Damietta University, New Dami- etta 34517, Egypt e-mail : r_elashwah@yahoo.com Mohamed Kamal Aouf Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt e-mail : mkaouf127@yahoo.com Ahmed Hassan and Alaa Hassan ∗ Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt e-mail : aam_hassan@yahoo.com, alaahassan1986@yahoo.com Abstract. In this paper we derive some results for certain new class of analytic functions defined by using Ruscheweyh derivative with varying arguments. 1. Introduction Let A denote the class of functions of the form: (1.1) f (z)= z + ∞ ∑ k=2 a k z k , which are analytic and univalent in the open unit disc U = {z ∈ C : |z| < 1}. Given * Corresponding Author. Received September 17, 2012; accepted April 22, 2013. 2010 Mathematics Subject Classification: 30C45. Keywords and Phrases: analytic functions, univalent, Hadamard product, Ruscheweyh derivative, extreme points. 453