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
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.