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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 375604, 8 pages
http://dx.doi.org/10.1155/2013/375604
Research Article

The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings

1Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand
2Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand

Received 3 June 2013; Accepted 31 July 2013

Academic Editor: Calogero Vetro

Copyright © 2013 Wutiphol Sintunavarat and Poom Kumam. 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 [7 citations]

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

  • Poom Kumam, Hassen Aydi, Erdal Karapinar, and Wutiphol Sintunavarat, “Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems,” Fixed Point Theory and Applications, 2013. View at Publisher · View at Google Scholar
  • Erdal Karapinar, and Wutiphol Sintunavarat, “The existence of optimal approximate solution theorems for generalized alpha-proximal contraction non-self mappings and applications,” Fixed Point Theory and Applications, 2013. View at Publisher · View at Google Scholar
  • Manuel De la Sen, Shyam Lal Singh, Madjid Eshaghi Gordji, Asier Ibeas, and Ravi P. Agarwal, “Best proximity and fixed point results for cyclic multivalued mappings under a generalized contractive condition,” Fixed Point Theory and Applications, 2013. View at Publisher · View at Google Scholar
  • P. Kumam, V. Pragadeeswarar, M. Marudai, and K. Sitthithakerngkiet, “Coupled best proximity points in ordered metric spaces,” Fixed Point Theory and Applications, 2014. View at Publisher · View at Google Scholar
  • Yaqiong Sun, Yongfu Su, and Jingling Zhang, “A new method for the research of best proximity point theorems of nonlinear mappings,” Fixed Point Theory and Applications, 2014. View at Publisher · View at Google Scholar
  • Marwan Amin Kutbi, Sumit Chandok, and Wutiphol Sintunavarat, “Optimal solutions for nonlinear proximal C-N-contraction mapping in metric space,” Journal of Inequalities and Applications, 2014. View at Publisher · View at Google Scholar
  • Chirasak Mongkolkeha, Chayut Kongban, and Poom Kumam, “Existence and Uniqueness of Best Proximity Points for Generalized Almost Contractions,” Abstract and Applied Analysis, vol. 2014, pp. 1–11, 2014. View at Publisher · View at Google Scholar