Generalized contractive set-valued maps on complete preordered quasi-metric spaces

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. ; 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. ; The authors thank the referees for some useful suggestions and corrections. This research is supported by the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01. S. Romaguera and P. Tirado also acknowledge the support of Universitat Politecnica de Valencia, Grant PAID-06-12. ; Marín Molina, J.; Romaguera Bonilla, S.; Tirado Peláez, P. (2013). Generalized contractive set-valued maps on complete preordered quasi-metric spaces. Journal of Function Spaces and Applications. 2013:1-6. https://doi.org/10.1155/2013/269246 ; S ; 1 ; 6 ; 2013 ; Ekeland, I. (1979). Nonconvex minimization problems. Bulletin of the American Mathematical Society, 1(3), 443-475. doi:10.1090/s0273-0979-1979-14595-6 ; Park, S. (2000). On generalizations of the Ekeland-type variational principles. Nonlinear Analysis: Theory, Methods & Applications, 39(7), 881-889. doi:10.1016/s0362-546x(98)00253-3 ; Al-Homidan, S., Ansari, Q. H., & Yao, J.-C. (2008). Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory. Nonlinear Analysis: Theory, Methods & Applications, 69(1), 126-139. doi:10.1016/j.na.2007.05.004 ; Marín, J., Romaguera, S., & Tirado, P. (2011). Weakly contractive multivalued maps and w-distances on complete quasi-metric spaces. Fixed Point Theory and Applications, 2011(1), 2. ...