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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 269246, 6 pages
http://dx.doi.org/10.1155/2013/269246
Research Article

Generalized Contractive Set-Valued Maps on Complete Preordered Quasi-Metric Spaces

Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain

Received 12 October 2012; Accepted 8 December 2012

Academic Editor: Gerald Beer

Copyright © 2013 J. Marín et al. 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.

Abstract

By using a suitable modification of the notion of a -distance we obtain some fixed point results for generalized contractive set-valued maps on complete preordered quasi-metric spaces. We also show that several distinguished examples of non-metrizable quasi-metric spaces and of cones of asymmetric normed spaces admit -distances of this type. Our results extend and generalize some well-known fixed point theorems.