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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 896912, 19 pages
Generalized Proximal -Contraction Mappings and Best Proximity Points
1Department of Mathematics, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom 73140, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, King Mongkut's, University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, Thailand
Received 19 July 2012; Accepted 24 September 2012
Academic Editor: Haiyun Zhou
Copyright © 2012 Winate Sanhan 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 [15 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.
- 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.
- Hemant Kumar Nashine, Poom Kumam, and Calogero Vetro, “Best proximity point theorems for rational proximal contractions,” Fixed Point Theory and Applications, 2013.
- M. De la Sen, and E. Karapinar, “Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations,” Abstract and Applied Analysis, vol. 2013, pp. 1–16, 2013.
- Wutiphol Sintunavarat, and Poom Kumam, “The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings,” Abstract and Applied Analysis, vol. 2013, pp. 1–8, 2013.
- N. Hussain, M. A. Kutbi, and P. Salimi, “Best Proximity Point Results for Modified --Proximal Rational Contractions,” Abstract and Applied Analysis, vol. 2013, pp. 1–14, 2013.
- Maryam A. Alghamdi, Naseer Shahzad, and Francesca Vetro, “Best Proximity Points for Some Classes of Proximal Contractions,” Abstract and Applied Analysis, vol. 2013, pp. 1–10, 2013.
- 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.
- Moosa Gabeleh, and Naseer Shahzad, “Existence and Uniqueness of a Solution for Some Nonlinear Programming Problems,” Mediterranean Journal of Mathematics, 2014.
- 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.
- V. Pragadeeswarar, M. Marudai, P. Kumam, and K. Sitthithakerngkiet, “The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 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.
- Moosa Gabeleh, “Best Proximity Points forWeak Proximal Contractions,” Bulletin Of The Malaysian Mathematical Sciences Society, vol. 38, no. 1, pp. 143–154, 2015.
- Manuel De la Sen, and Erdal Karapınar, “Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces,” Journal of Function Spaces, vol. 2015, pp. 1–11, 2015.
- Peyman Salimi, and Pasquale Vetro, “A Best Proximity Point Theorem for Generalized Geraghty-Suzuki Contractions,” Bulletin Of The Malaysian Mathematical Sciences Society, vol. 39, no. 1, pp. 245–256, 2016.