Fixed Point Theory and Applications 
Volume 2006 (2006), Article ID 61623, 10 pages
doi:10.1155/FPTA/2006/61623

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

Abstract

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.