FIXED POINT THEOREMS IN GENERATING SPACES OF QUASI-NORM FAMILY AND APPLICATIONS

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. Copyright © 2006 J.-Z. Xiao and X.-H. Zhu. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distribu-tion, and reproduction in any medium, provided the original work is properly cited. 1