Open Access

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

Fixed Point Theory and Applications20062006:61623

DOI: 10.1155/FPTA/2006/61623

Received: 11 April 2005

Accepted: 21 November 2005

Published: 26 February 2006

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Nanjing University of Information Science and Technology

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Copyright

© J.-Z. Xiao and X.-H. Zhu. 2006

This article is published under license to BioMed Central Ltd. 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.