Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2011, Article ID 542941, 17 pages
http://dx.doi.org/10.1155/2011/542941
Research Article

On a General Contractive Condition for Cyclic Self-Mappings

Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, Campus de Leioa (Bizkaia), Apartado 644 de Bilbao, 48080 Bilbao, Spain

Received 26 April 2011; Accepted 3 October 2011

Academic Editor: J. C. Butcher

Copyright © 2011 M. De la Sen. 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. R. Bhardwaj, S. S. Rajput, and R. N. Yadava, β€œApplication of fixed point theory in metric spaces,” Thai Journal of Mathematics, vol. 5, no. 2, pp. 253–259, 2007. View at Google Scholar Β· View at Zentralblatt MATH
  2. J. Harjani, B. López, and K. Sadarangani, β€œA 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 Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. W. A. Kirk, P. S. Srinivasan, and P. Veeramani, β€œFixed points for mappings satisfying cyclical contractive conditions,” Fixed Point Theory, vol. 4, no. 1, pp. 79–89, 2003. View at Google Scholar Β· View at Zentralblatt MATH
  4. A. A. Eldred and P. Veeramani, β€œExistence and convergence of best proximity points,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1001–1006, 2006. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  5. S. Karpagam and S. Agrawal, β€œBest proximity point theorems for p-cyclic Meir-Keeler contractions,” Fixed Point Theory and Applications, vol. 2009, Article ID 197308, 9 pages, 2009. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  6. C. Di Bari, T. Suzuki, and C. Vetro, β€œBest proximity points for cyclic Meir-Keeler contractions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 11, pp. 3790–3794, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. M. De la Sen, β€œLinking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings,” Fixed Point Theory and Applications, vol. 2010, Article ID 572057, 23 pages, 2010. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  8. X. Qin, S. M. Kang, and R. P. Agarwal, β€œOn the convergence of an implicit iterative process for generalized asymptotically quasi-nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2010, Article ID 714860, 19 pages, 2010. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  9. V. Azhmyakov, β€œConvexity of the set of fixed points generated by some control systems,” Journal of Applied Mathematics, vol. 2009, Article ID 291849, 14 pages, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  10. M. De la Sen and R. P. Agarwal, β€œSome fixed-point results for a class of extended cyclic self-mappings with a more general contractive condition,” Fixed Point Theory and Applications, vol. 2011: 59, 2001. View at Publisher Β· View at Google Scholar
  11. M. De la Sen, β€œSome combined relations between contractive mappings, Kannan mappings, reasonable expansive mappings, and T-stability,” Fixed Point Theory and Applications, vol. 2009, Article ID 815637, 25 pages, 2009. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  12. Y. Enjouji, M. Nakanishi, and T. Suzuki, β€œA generalization of Kannan's fixed point theorem,” Fixed Point Theory and Applications, vol. 2009, Article ID 192872, 10 pages, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  13. S. Banach, β€œSur les operations dans les ensembles abstracts et leur application aux équations intégrales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922. View at Google Scholar
  14. S. K. Chaterjee, β€œFixed-point theorems,” Comptes Rendus de l'Académie Bulgare des Sciences, vol. 25, pp. 727–730, 1972. View at Google Scholar Β· View at Zentralblatt MATH
  15. B. Fisher, β€œA fixed-point theorem for compact metric spaces,” Publicationes Mathematicae, vol. 25, no. 3-4, pp. 193–194, 1978. View at Google Scholar Β· View at Zentralblatt MATH
  16. R. Kannan, β€œSome results on fixed points,” Bulletin of the Calcutta Mathematical Society, vol. 60, pp. 71–76, 1968. View at Google Scholar Β· View at Zentralblatt MATH
  17. R. Kannan, β€œSome results on fixed points. II,” The American Mathematical Monthly, vol. 76, pp. 405–408, 1969. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  18. S. Reich, β€œSome remarks concerning contraction mappings,” Canadian Mathematical Bulletin, vol. 14, pp. 121–124, 1971. View at Google Scholar Β· View at Zentralblatt MATH
  19. M. Kikkawa and T. Suzuki, β€œSome similarity between contractions and Kannan mappings,” Fixed Point Theory and Applications, vol. 2008, Article ID 649749, 8 pages, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  20. P. V. Subrahmanyam, β€œCompleteness and fixed-points,” vol. 80, no. 4, pp. 325–330, 1975. View at Google Scholar Β· View at Zentralblatt MATH