International Journal of Differential Equations
Volume 2009 (2009), Article ID 737129, 13 pages
doi:10.1155/2009/737129
Research Article

Double Integral Operators Concerning Starlike of Order β

Kazuo Kuroki and Shigeyoshi Owa

Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan

Received 16 March 2009; Accepted 31 May 2009

Academic Editor: Stevo Stevic

Copyright © 2009 Kazuo Kuroki and Shigeyoshi Owa. 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.

Abstract

Double integral operators which were considered by S. S. Miller and P. T. Mocanu (Integral Transform. Spec. Funct. 19(2008), 591–597) are discussed. In order to show the analytic function f(z) is starlike of order β in the open unit disk 𝕌, the theory of differential subordinations for analytic functions is applied. The object of the present paper is to discuss some interesting conditions for f(z) to be starlike of order β in 𝕌 concerned with second-order differential inequalities and double integral operators.