Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 61623, 10 pages

Fixed point theorems in generating spaces of quasi-norm family and applications

Jian-Zhong Xiao and Xing-Hua Zhu

Department of Mathematics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received 11 April 2005; Accepted 21 November 2005

Copyright © 2006 Jian-Zhong Xiao and Xing-Hua Zhu. 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.


Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fixed point theorems in Menger probabilistic normed spaces and fuzzy normed spaces are obtained.