Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Subordination Result Associated with Certain Subclass of Analytic Functions Involving Salagean Operator | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 48294 6 pages doi 2007 48294 Research Article On Subordination Result Associated with Certain Subclass of Analytic Functions Involving Salagean Operator Sevtap Sumer Eker Bilal Seker and Shigeyoshi Owa Received 3 February 2007 Accepted 15 May 2007 Recommended by Narendra K. Govil We obtain an interesting subordination relation for Salagean-type certain analytic functions by using subordination theorem. Copyright 2007 Sevtap Sumer Eker et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Let denote the class of functions f z normalized by 00 f z z ữjZj j 2 which are analytic in the open unit disk U z e C z 1 . We denote by a a and 3t a 0 a 1 the class of starlike functions of order a and the class of convex functions of order a respectively where y a if e Re ậ a z e 4 f z a if e Re 1 zf z a z e 4 f z Note that f z e 3t a o zf z e y a . 2 Journal of Inequalities and Applications Salagean 1 has introduced the following operator D f z f z D1 f z Df z zf z Dnf z D Dn-1 f z n e No 0 u 1 2 . . We note that Dnf z z ffiaffi n e No N u 0 . 1 2 We denote by Sn a subclass of the class which is defined as follows Sn a Dn 1 f z f f e Re az e U 0 a 1 . L L Dnf z J J The class Sn a was introduced by Kadioglu 2 . We begin by recalling following coefficient inequality associated with the function class Sn a . Theorem Kadioglu 2 . If f z e tâ defined by satisfies the coefficient inequality X jn 1 - ajn ịafi 1 - a 0 a 1 2 then f z e Sn a . In view of Theorem we now introduce the subclass Sn a c Sn a which consists of functions f z e whose Taylor-Maclaurin coefficients satisfy the inequality . In this paper we prove an interesting subordination result for the class
