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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 189567, 3 pages
http://dx.doi.org/10.1155/2013/189567
Research Article

A Note on Some Best Proximity Point Theorems Proved under P-Property

1Department of Mathematics, Imam Khomeini International University, Qazvin 34149, Iran
2Department of Mathematics, Ayatollah Boroujerdi University, Borujerd, Iran

Received 20 July 2013; Accepted 29 September 2013

Academic Editor: Mohamed Jleli

Copyright © 2013 Ali Abkar and Moosa Gabeleh. 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. V. S. Raj, “A best proximity point theorem for weakly contractive non-self-mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 14, pp. 4804–4808, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Abkar and M. Gabeleh, “Best proximity points of non-self mappings,” TOP, vol. 21, no. 2, pp. 287–295, 2013. View at Publisher · View at Google Scholar · View at Scopus
  3. B. Samet, “Some results on best proximity point theorem,” Journal of Optimization Theory and Applications, vol. 159, no. 1, pp. 281–291, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Abkar and M. Gabeleh, “The existence of best proximity points for multivalued non-self-mappings,” Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales A, vol. 107, no. 2, pp. 319–325, 2013. View at Publisher · View at Google Scholar
  5. J. Caballero, J. Harjani, and K. Sadarangani, “A best proximity point theorem for Geraghty-contractions,” Fixed Point Theory and Applications, vol. 2012, article 231, 2012. View at Publisher · View at Google Scholar
  6. M. Gabeleh, “Proximal weakly contractive and proximal nonexpansive non-self-mappings in metric and Banach spaces,” Journal of Optimization Theory and Applications, vol. 158, no. 2, pp. 615–625, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. B. E. Rhoades, “Some theorems on weakly contractive maps,” Nonlinear Analysis, Theory, Methods and Applications, vol. 47, no. 4, pp. 2683–2693, 2001. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Meir and E. Keeler, “A theorem on contraction mappings,” Journal of Mathematical Analysis and Applications, vol. 28, pp. 326–329, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. B. Nadler, Jr., “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, pp. 475–488, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. A. Geraghty, “On contractive mappings,” Proceedings of the American Mathematical Society, vol. 40, pp. 604–608, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet