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 A New Subclass of Analytic Functions Involving Al-Oboudi Differential Operator | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 452057 10 pages doi 2008 452057 Research Article A New Subclass of Analytic Functions Involving Al-Oboudi Differential Operator Sevtap Sumer Eker and H. Ozlem Guney Department of Mathematics Faculty of Science and Letters Dicle University 21280 Diyarbakir Turkey Correspondence should be addressed to Sevtap Sumer Eker sevtaps@ Received 25 September 2007 Accepted 4 February 2008 Recommended by Jozsef Szabados The main object of this paper is to introduce and investigate a new subclass of normalized analytic functions in the open unit disc U which is defined by Al-Oboudi differential operator. Coefficient inequalities extreme points and integral means inequalities for fractional derivative for this class are given. Copyright 2008 S. Sumer Eker and H. Ozlem Guney. 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 and definitions Let A denote the class of functions f normalized by f z - z g a j which are analytic in the open unit disc U z z 1 . For f A Al-Oboudi 1 introduced the following operator Df z f z D1f z 1 - 6 f z ôzffz Def z e 0 Dnf z De Dn-1f z n N 1 2 3 . . If f is given by then from and we see that Dnf z z Ệ 1 j - 1 e najzj n N0 N u 0 . When e 1 we get Salagean differential operator 2 . 2 Journal of Inequalities and Applications Definition . Let Sm n 0 a denote the subclass of A consisting of functions f which satisfy the inequality Re Dmf z f a for some 0 a 1 m G N n G N0 and all z G U. The object of the present paper is to investigate the coefficient bounds extreme points and integral mean inequalities for fractional derivatives of functions belonging to the class Sm n s a . 2. Coefficient inequalities Our first theorem gives a .
