tailieunhanh - Báo cáo hóa học: " Research Article New Classes of Analytic Functions Involving Generalized Noor Integral 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 New Classes of Analytic Functions Involving Generalized Noor Integral Operator | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 390435 14 pages doi 2008 390435 Research Article New Classes of Analytic Functions Involving Generalized Noor Integral Operator Rabha W. Ibrahim and Maslina Darus School of Mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia Selangor Darul Ehsan Bangi 43600 Malaysia Correspondence should be addressed to Maslina Darus maslina@ Received 22 March 2008 Accepted 25 April 2008 Recommended by Jozsef Szabados The present article investigates new classes of functions involving generalized Noor integral operator. Some properties of these functions are studied including characterization and distortion theorems. Moreover we illustrate sufficient conditions for subordination and superordination for analytic functions. Copyright 2008 R. W. Ibrahim and M. Darus. 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 preliminaries Let H be the class of functions analytic in U and let H a n be the subclass of H consisting of functions of the form f z a anzn an 1zn 1 . Let A be the subclass of H consisting of functions of the form f z z a2z2 . Denote by Da A A the operator defined by z D 1 f z a -1 1 - z a 1 J where refers to the Hadamard product or convolution. Then implies that z zn1f Dnf z -----n n G No N u 0 . We note that D f z f z and D f z zf fz . The operator Dnf is called Ruscheweyh derivative of nth order of f. Noor 1 2 defined and studied an integral operator In A A analogous to Dnf as follows. 2 Journal of Inequalities and Applications Let fn z z 1 - z n 1 n G No and let f be defined such that fn z f -1 z -. 1 z Then Inf z fn 11 z f z z 1 z n 1 1 f z - Note that I0f z zf z and If z f z . The operator In is called the Noor Integral