College of Mathematics and Statistics, Chongqing University, Chongqing 400030, China
Copyright © 2010 Deqiang Liu and Hu Yang. 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.
Both Djordjević (2007) and Takane et al. (2007) have studied the equivalent conditions for and . In this note, we derive the necessary and sufficient conditions for , , and .