Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Coefficient, distortion and growth inequalities for certain close-to-convex functions | Cho et al. Journal of Inequalities and Applications 2011 2011 100 http content 2011 1 100 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Coefficient distortion and growth inequalities for certain close-to-convex functions Nak Eun Cho 1 Oh Sang Kwon2 and V Ravichandran3 4 Correspondence necho@. kr department of Applied Mathematics Pukyong National University Busan 608-737 South Korea Full list of author information is available at the end of the article Springer Abstract In the present investigation certain subclasses of close-to-convex functions are investigated. In particular we obtain an estimate for the Fekete-Szego functional for functions belonging to the class distortion growth estimates and covering theorems. Mathematics Subject Classification 2010 30C45 30C80. Keywords starlike functions close-to-convex functions Fekete-Szego inequalities distortion and growth theorems subordination theorem 1 Introduction Let ID z eC z 1 be the open unit disk in the complex plane c. Let A be the class of analytic functions defined on 0 and normalized by the conditions f 0 0 and f 0 1. Let 5 be the subclass of A consisting of univalent functions 1 . Sakaguchi 2 introduced a class of functions called starlike functions with respect to symmetric points they are the functions f e A satisfying the condition zf z Re 0 - f z - f -z 0. These functions are close-to-convex functions. This can be easily seen by showing that the function f z -f -z 2 is a starlike function in ID. Motivated by the class of starlike functions with respect to symmetric points Gao and Zhou 3 discussed a class Ks of close-to-convex univalent functions. A function f e Ks if it satisfies the following inequality Ref -fA 0 z et g z g -z for some function g e S 1 2 . The idea here is to replace the average of fz and - f -z by the corresponding product -g z g -z and the factor z is included to normalize the expression so .
