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Journal of Function Spaces
Volume 2015, Article ID 865069, 9 pages
Research Article

The Singular Points of Analytic Functions with Finite -Order Defined by Laplace-Stieltjes Transformations

1Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi 333403, China
2Beijing Key Laboratory of Information Service Engineering, Department of General Education, Beijing Union University, No. 97 Bei Si Huan Dong Road, Chaoyang District, Beijing 100101, China

Received 19 April 2014; Accepted 18 July 2014

Academic Editor: Seppo Hassi

Copyright © 2015 Hong-Yan Xu and Zu-Xing Xuan. 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.


We study the singular points of analytic functions defined by Laplace-Stieltjes transformations which converge on the right half plane, by introducing the concept of -order functions. We also confirm the existence of the finite -order Borel points of such functions and obtained the extension of the finite -order Borel point of two analytic functions defined by two Laplace-Stieltjes transformations convergent on the right half plane. The main results of this paper are improvement of some theorems given by Shang and Gao.