tailieunhanh - Báo cáo hóa học: "Research Article A New General Integral Operator Defined by Al-Oboudi Differential Operator"

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 General Integral Operator Defined by Al-Oboudi Differential Operator | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 158408 13 pages doi 2009 158408 Research Article A New General Integral Operator Defined by Al-Oboudi Differential Operator Serap Bulut Civil Aviation College Kocaeli University Arslanbey Campus 41285 Izmit-Kocaeli Turkey Correspondence should be addressed to Serap Bulut Received 8 December 2008 Accepted 22 January 2009 Recommended by Narendra Kumar Govil We define a new general integral operator using Al-Oboudi differential operator. Also we introduce new subclasses of analytic functions. Our results generalize the results of Breaz Guney and Salagean. Copyright 2009 Serap Bulut. 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 A denote the class of functions of the form TO f z z y UnZn which are analytic in the open unit disk U z e C z 1 and S f e A f is univalent in U . For f e A Al-Oboudi 1 introduced the following operator Df z f z D1f z 1 - X f z Xzf z Dxf z X 0 Dkf z DẰ pk-1f z k e N 1 2 3 . . 2 Journal of Inequalities and Applications If f is given by then from and we see that TO Dkf z z 1 n - 1 l kanzn k e No N u 0 with Dkf 0 0. Remark . When A 1 we get Salagean s differential operator 2 . Now we introduce new classes Sk 0 b A and Kk 0 b A as follows. A function f e A is in the classes Sk 6 b A where 6 e 0 1 b e C- 0 A 0 k e N0 if and only if or equivalently rJ1 V Df b Dkf z 6 Re 1 tfzf b Dkf z for all z e U. A function f eA is in the classs Kk 6 b A where 6 e 0 1 b e C- 0 A 0 k e N0 if and only if Re 1 Af 1 I b Dkf z I 6 for all z e U. We note that f e Kk 6 b A if and only if zf e Sk 6 b A . Remark . i For k 0 and A 1 we have the classes So 6 b 1 S6 b Ko 6 b 1 C6 b introduced by Frasin 3 . ii For