Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2015, Article ID 361657, 6 pages
http://dx.doi.org/10.1155/2015/361657
Research Article

Best Proximity Points for Generalized Proximal Weak Contractions Satisfying Rational Expression on Ordered Metric Spaces

Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamil Nadu 620 024, India

Received 26 July 2014; Accepted 6 September 2014

Academic Editor: Poom Kumam

Copyright © 2015 V. Pragadeeswarar and M. Marudai. 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. A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 1435–1443, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. M. S. Khan, M. Swaleh, and S. Sessa, “Fixed point theorems by altering distances between the points,” Bulletin of the Australian Mathematical Society, vol. 30, no. 1, pp. 1–9, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  4. D. S. Jaggi, “Some unique fixed point theorems,” Indian Journal of Pure and Applied Mathematics, vol. 8, no. 2, pp. 223–230, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Harjani, B. López, and K. Sadarangani, “A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space,” Abstract and Applied Analysis, vol. 2010, Article ID 190701, 8 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. N. V. Luong and N. X. Thuan, “Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 46, 2011. View at Google Scholar · View at MathSciNet
  7. K. Fan, “Extensions of two fixed point theorems of F. E. Browder,” Mathematische Zeitschrift, vol. 112, pp. 234–240, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. M. de la Sen and R. P. Agarwal, “Some fixed point-type results for a class of extended cyclic self-mappings with a more general contractive condition,” Fixed Point Theory and Applications, vol. 2011, article 59, 2011. View at Google Scholar · View at MathSciNet
  9. P. S. Srinivasan and P. Veeramani, “On existence of equilibrium pair for constrained generalized games,” Fixed Point Theory and Applications, no. 1, pp. 21–29, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. A. A. Eldred and P. Veeramani, “Existence and convergence of best proximity points,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1001–1006, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. M. A. Al-Thagafi and N. Shahzad, “Convergence and existence results for best proximity points,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 10, pp. 3665–3671, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. Sadiq Basha and P. Veeramani, “Best proximity pair theorems for multifunctions with open fibres,” Journal of Approximation Theory, vol. 103, no. 1, pp. 119–129, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. W. K. Kim and K. H. Lee, “Existence of best proximity pairs and equilibrium pairs,” Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp. 433–446, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. W. A. Kirk, S. Reich, and P. Veeramani, “Proximinal retracts and best proximity pair theorems,” Numerical Functional Analysis and Optimization, vol. 24, no. 7-8, pp. 851–862, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. 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 MathSciNet · View at Scopus
  16. E. Karapnar, V. Pragadeeswarar, and M. Marudai, “Best proximity point for generalized proximal weak contractions in complete metric space,” Journal of Applied Mathematics, vol. 2014, Article ID 150941, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S. S. Basha, “Discrete optimization in partially ordered sets,” Journal of Global Optimization, vol. 54, no. 3, pp. 511–517, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. A. Abkar and M. Gabeleh, “Best proximity points for cyclic mappings in ordered metric spaces,” Journal of Optimization Theory and Applications, vol. 150, no. 1, pp. 188–193, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. A. Abkar and M. Gabeleh, “Generalized cyclic contractions in partially ordered metric spaces,” Optimization Letters, vol. 6, no. 8, pp. 1819–1830, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. P. Kumam, V. Pragadeeswarar, M. Marudai, and K. Sitthithakerngkiet, “Coupled best proximity points in ordered metric spaces,” Fixed Point Theory and Applications, vol. 2014, article 107, 2014. View at Publisher · View at Google Scholar · View at Scopus
  21. V. Pragadeeswarar and M. Marudai, “Best proximity points: approximation and optimization in partially ordered metric spaces,” Optimization Letters, vol. 7, no. 8, pp. 1883–1892, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. V. Pragadeeswarar and M. Marudai, “Best proximity points for generalized proximal weak contractions in partially ordered metric spaces,” Optimization Letters, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  23. 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, Article ID 274062, 7 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. H. K. Nashine, P. Kumam, and C. Vetro, “Best proximity point theorems for rational proximal contractions,” Fixed Point Theory and Applications, vol. 2013, article 95, 2013. View at Publisher · View at Google Scholar · View at MathSciNet