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Báo cáo hóa học: " Research Article A New Subclass of Analytic Functions Defined by Generalized Ruscheweyh 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 Subclass of Analytic Functions Defined by Generalized Ruscheweyh Differential Operator | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 134932 12 pages doi 10.1155 2008 134932 Research Article A New Subclass of Analytic Functions Defined by Generalized Ruscheweyh Differential Operator Serap Bulut Civil Aviation College Kocaeli University Arslanbey Campus 41285 Izmit-Kocaeli Turkey Correspondence should be addressed to Serap Bulut serap.bulut@kocaeli.edu.tr Received 1 July 2008 Accepted 3 September 2008 Recommended by Narendra Kumar Govil We investigate a new subclass of analytic functions in the open unit disk U which is defined by generalized Ruscheweyh differential operator. Coefficient inequalities extreme points and the integral means inequalities for the fractional derivatives of order p n 0 p n 0 n 1 of functions belonging to this subclass are obtained. Copyright 2008 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 Throughout this paper we use the following notations N 1 2 3 . No N u 0 . _ Í1.1 R 1 u G R u 1 R01 R 1 0 . Let A denote the class of all functions of the form f z z anzn 1.2 n 2 which are analytic in the open unit disk U z G C z 1 . For fj G A given by TO fj z z zan jzn j 1 2 C1.3 n 2 2 Journal of Inequalities and Applications the Hadamard product or convolution f1 f2 of f1 and f2 is defined by TO f1 f2 z z 2 an 1an 2Zn. n 2 1.4 Using the convolution 1.4 Shaqsi and Darus 1 introduced the generalization of the Ruscheweyh derivative as follows. For f eA A 0 and u e R-1 we consider . z RUf Rf z z e U Ơ - z 1.5 where RAf z 1 - Af z Azf z z e U. If f e A is of the form 1.2 then we obtain the power series expansion of the form Rf z z 1 n - 1 X C u n anzn n 2 1.6 where CM ff -1 n e N 1.7 and where a n is the Pochhammer symbol or shifted factorial defined in terms of the Gamma function by x r a n 1 if n 0 a