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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 375604, 8 pages
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 [10 citations]
The following is the list of published articles that have cited the current article.
- 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.
- 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.
- 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.
- P. Kumam, V. Pragadeeswarar, M. Marudai, and K. Sitthithakerngkiet, “Coupled best proximity points in ordered metric spaces,” Fixed Point Theory and Applications, 2014.
- 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.
- 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.
- Wutiphol Sintunavarat Poom Kumam, “The existence and convergence of best proximity points for generalized proximal contraction mappings,” Fixed Point Theory And Applications, 2014.
- 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.
- M. De La Sen, and Asier Ibeas, “Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces,” Abstract and Applied Analysis, vol. 2014, pp. 1–11, 2014.
- Sujitra Sanhan, and Chirasak Mongkolkeha, “Convergence and best proximity points for Berinde's cyclic contraction with proximally complete property,” Mathematical Methods in the Applied Sciences, 2016.