Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2017, Article ID 4901762, 7 pages
https://doi.org/10.1155/2017/4901762
Research Article

On Topological Properties of Metrics Defined via Generalized “Linking Construction”

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Ul. Umultowska 87, 61-614 Poznań, Poland

Correspondence should be addressed to Marcin Borkowski; lp.ude.uma@krobm

Received 2 May 2017; Accepted 25 October 2017; Published 21 November 2017

Academic Editor: P. Veeramani

Copyright © 2017 Marcin Borkowski 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.

Linked References

  1. M. Borkowski, D. Bugajewski, and H. Przybycień, “Hyperconvex spaces revisited,” Bulletin of the Australian Mathematical Society, vol. 68, no. 2, pp. 191–203, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. Borkowski, Theory of Hyperconvex Metric Spaces. A Beginner’s Guide, vol. 14 of Lecture Notes in Nonlinear Analysis, Juliusz Schauder Center for Nonlinear Studies, Toruń, Poland, 2015. View at MathSciNet
  3. R. Espínola and M. A. Khamsi, “Introduction to hyperconvex spaces,” in Handbook of Metric Fixed Point Theory, W. A. Kirk and B. Sims, Eds., Kluwer Academic Publishers, Dordrecht, Netherlands, 2001. View at Google Scholar
  4. D. Bugajewski and E. Grzelaczyk, “A fixed point theorem in hyperconvex spaces,” Archiv der Mathematik, vol. 75, no. 5, pp. 395–400, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. W. A. Kirk, “Hyperconvexity of -trees,” Fundamenta Mathematicae, vol. 156, no. 1, pp. 67–72, 1998. View at Google Scholar · View at MathSciNet
  6. J. C. Mayer and L. G. Oversteegen, “A topological characterization of -trees,” Transactions of the American Mathematical Society, vol. 320, no. 1, pp. 395–415, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  7. F. Rimlinger, “Free actions on -trees,” Transactions of the American Mathematical Society, vol. 332, no. 1, pp. 313–329, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  8. A. G. Aksoy and B. Maurizi, “Metric trees, hyperconvex hulls and extensions,” Turkish Journal of Mathematics, vol. 32, no. 2, pp. 219–234, 2008. View at Google Scholar · View at MathSciNet
  9. W. B. Johnson, J. Lindenstrauss, D. Preiss, and G. Schechtman, “Lipschitz quotients from metric trees and from Banach spaces containing ,” Journal of Functional Analysis, vol. 194, no. 2, pp. 332–346, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  10. M. Borkowski, D. Bugajewski, and D. Phulara, “On some properties of hyperconvex spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 213812, pp. 1–19, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. Á. Száz, “A common generalization of the postman, radial, and river metrics,” Rostocker Mathematisches Kolloquium, vol. 67, pp. 89–125, 2012. View at Google Scholar
  12. D. Bugajewski and E. Grzelaczyk, “On the measures of noncompactness in some metric spaces,” New Zealand Journal of Mathematics, vol. 27, no. 2, pp. 177–182, 1998. View at Google Scholar · View at MathSciNet
  13. J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, vol. 60 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1980. View at MathSciNet
  14. D. Bugajewski, “Some remarks on Kuratowski’s measure of noncompactness in vector spaces with a metric,” Commentationes Mathematicae. Prace Matematyczne, vol. 32, pp. 5–9, 1992. View at Google Scholar · View at MathSciNet