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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 713252, 10 pages
http://dx.doi.org/10.1155/2013/713252
Research Article

Best Proximity Points for Some Classes of Proximal Contractions

1Department of Mathematics, King Abdulaziz University, Science Faculty for Girls, P.O. Box 4087, Jeddah 21491, Saudi Arabia
2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21859, Saudi Arabia
3DEIM, Università Degli Studi di Palermo, Viale Delle Scienze, 90128 Palermo, Italy

Received 9 May 2013; Revised 11 August 2013; Accepted 11 August 2013

Academic Editor: E. Karapinar

Copyright © 2013 Maryam A. Alghamdi 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.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • Tomonari Suzuki, “The existence of best proximity points with the weak P-property,” Fixed Point Theory and Applications, 2013. View at Publisher · View at Google Scholar
  • Jingling Zhang, and Yongfu Su, “Best proximity point theorems for weakly contractive mapping and weakly Kannan mapping in partial metric spaces,” Fixed Point Theory and Applications, 2014. View at Publisher · View at Google Scholar
  • Moosa Gabeleh, and Naseer Shahzad, “Existence and Uniqueness of a Solution for Some Nonlinear Programming Problems,” Mediterranean Journal of Mathematics, 2014. View at Publisher · View at Google Scholar
  • Poom Kumam, and Antonio Francisco Roldán López de Hierro, “On Existence and Uniqueness of -Best Proximity Points under -Contractivity Conditions and Consequences,” Abstract and Applied Analysis, vol. 2014, pp. 1–14, 2014. View at Publisher · View at Google Scholar
  • Poom Kumam, Peyman Salimi, and Calogero Vetro, “Best proximity point results for modified α-proximal C-contraction mappings,” Fixed Point Theory and Applications, vol. 2014, no. 1, pp. 99, 2014. View at Publisher · View at Google Scholar
  • Fairouz Tchier, Calogero Vetro, and Francesca Vetro, “Best approximation and variational inequality problems involving a simulation function,” Fixed Point Theory and Applications, vol. 2016, no. 1, 2016. View at Publisher · View at Google Scholar
  • Kishin Sadarangani, Erdal Karapinar, and Antonio-Francisco Roldán-López-De-Hierro, “Existence and uniqueness of best proximity points under rational contractivity conditions,” Mathematica Slovaca, vol. 66, no. 6, pp. 1427–1442, 2016. View at Publisher · View at Google Scholar
  • Leila Gholizadeh, and Erdal Karapınar, “Best proximity point results in dislocated metric spaces via R-functions,” Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017. View at Publisher · View at Google Scholar
  • Hüseyin Işık, M. Sangurlu Sezen, and Calogero Vetro, “$$\varphi $$ φ -Best proximity point theorems and applications to variational inequality problems,” Journal of Fixed Point Theory and Applications, 2017. View at Publisher · View at Google Scholar
  • Mohadeshe Paknazar, and Manuel Sen, “Best Proximity Point Results in Non-Archimedean Modular Metric Space,” Mathematics, vol. 5, no. 2, pp. 23, 2017. View at Publisher · View at Google Scholar