International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 3, Pages 435-439
Fixed point theorems for -complete topological spaces I
Department of Mathematics, University of Missouri at Rolla, Rolla 65401, Missouri, USA
Received 7 May 1991
Copyright © 1992 Troy L. Hicks. 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.
Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include -complete symmetric (semi-metric) spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality.