Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 287492, 13 pages
http://dx.doi.org/10.1155/2014/287492
Research Article

Discussion on “Multidimensional Coincidence Points” via Recent Publications

1Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey
3University of Jaén, Campus las Lagunillas s/n, 23071 Jaén, Spain

Received 17 March 2014; Accepted 23 March 2014; Published 8 May 2014

Academic Editor: Jen-Chih Yao

Copyright © 2014 Saleh A. Al-Mezel 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.

Linked References

  1. D. Guo and V. Lakshmikantham, “Coupled fixed points of nonlinear operators with applications,” Nonlinear Analysis, vol. 11, no. 5, pp. 623–632, 1987. View at Google Scholar · View at Scopus
  2. T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis, Theory, Methods and Applications, vol. 65, no. 7, pp. 1379–1393, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. V. Lakshmikantham and L. Ćirić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 70, no. 12, pp. 4341–4349, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. V. Berinde and M. Borcut, “Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 15, pp. 4889–4897, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. E. Karapınar, “Quartet fixed point for nonlinear contraction,” http://arxiv.org/abs/1106.5472.
  6. E. Karapınar and N. V. Luong, “Quadruple fixed point theorems for nonlinear contractions,” Computers and Mathematics with Applications, vol. 64, no. 6, pp. 1839–1848, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. E. Karapınar, “Quadruple fixed point theorems for weak ϕ-contractions,” ISRN Mathematical Analysis, vol. 2011, Article ID 989423, 15 pages, 2011. View at Publisher · View at Google Scholar
  8. S. Dalal, M. A. Khan, and S. Chauhan, “n-tupled coincidence point theorems in partially ordered metric spaces for compatible mappings,” Abstract and Applied Analysis, vol. 2014, Article ID 614019, 8 pages, 2014. View at Publisher · View at Google Scholar
  9. M. Imdad, A. H. Soliman, B. S. Choudhury, and P. Das, “On n-tupled coincidence point results in metric spaces,” Journal of Operators, vol. 2013, Article ID 532867, 8 pages, 2013. View at Publisher · View at Google Scholar
  10. E. Karapınar and A. Roldán, “A note on ‘N-fixed point theorems for nonlinear contractions in partially ordered metric spaces’,” Fixed Point Theory and Applications, vol. 2013, p. 310, 2013. View at Publisher · View at Google Scholar
  11. M. E. Gordji, Y. J. Cho, S. Ghods, M. Ghods, and M. H. Dehkordi, “Coupled fixed-point theorems for contractions in partially ordered metric spaces and applications,” Mathematical Problems in Engineering, vol. 2012, Article ID 150363, 20 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Berzig and B. Samet, “An extension of coupled fixed point's concept in higher dimension and applications,” Computers and Mathematics with Applications, vol. 63, no. 8, pp. 1319–1334, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. A. Roldán, J. Martínez-Moreno, and C. Roldán, “Multidimensional fixed point theorems in partially ordered complete metric spaces,” Journal of Mathematical Analysis and Applications, vol. 396, no. 2, pp. 536–545, 2012. View at Google Scholar
  14. A. Roldán, J. Martínez-Moreno, C. Roldán, and E. Karapınar, “Multidimensional fixed-point theorems in partially ordered complete partial metric spaces under (ψ,ϕ)-contractivity conditions,” Abstract and Applied Analysis, vol. 2013, Article ID 634371, 12 pages, 2013. View at Publisher · View at Google Scholar
  15. E. Karapınar, A. Roldán, J. Martínez-Moreno, and C. Roldán, “Meir-Keeler type multidimensional fixed point theorems in partially ordered metric spaces,” Abstract and Applied Analysis, vol. 2013, Article ID 406026, 9 pages, 2013. View at Publisher · View at Google Scholar
  16. A. Roldán, J. Martínez-Moreno, C. Roldán, and E. Karapınar, “Some remarks on multidimensional fixed point theorems,” Fixed Point Theory. In press.
  17. H. Aydi, E. Karapınar, and M. Zead, “Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces,” Tamkang J. Math., vol. 44, no. 3, pp. 233–251, 2013. View at Google Scholar
  18. E. Karapınar and V. Berinde, “Quadruple fixed point theorems for nonlinear contractions in partially ordered metric spaces,” Banach Journal of Mathematical Analysis, vol. 6, no. 1, pp. 74–89, 2012. View at Google Scholar · View at Scopus
  19. Z. Mustafa, H. Aydi, and E. Karapınar, “On common fixed points in G-metric spaces using (E.A) property,” Computers and Mathematics with Applications, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Ertürk and V. Karakaya, “n-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces,” Journal of Inequalities and Applications, vol. 2013, p. 196, 2013. View at Publisher · View at Google Scholar
  21. M. Ertürk and V. Karakaya, “Correction: ‘n-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces’,” Journal of Inequalities and Applications, vol. 2013, p. 368, 2013. View at Publisher · View at Google Scholar
  22. E. Karapınar and A. Roldán, “A note on ‘n-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces’,” Journal of Inequalities and Applications, vol. 2013, p. 567, 2013. View at Publisher · View at Google Scholar
  23. V. Berinde, “Coupled fixed point theorems for φ-contractive mixed monotone mappings in partially ordered metric spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 75, no. 6, pp. 3218–3228, 2012. View at Publisher · View at Google Scholar · View at Scopus
  24. B. S. Choudhury and A. Kundu, “A coupled coincidence point result in partially ordered metric spaces for compatible mappings,” Nonlinear Analysis, Theory, Methods and Applications, vol. 73, no. 8, pp. 2524–2531, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. N. V. Luong and N. X. Thuan, “Coupled fixed point theorems for mixed monotone mappings and an application to integral equations,” Computers and Mathematics with Applications, vol. 62, no. 11, pp. 4238–4248, 2011. View at Publisher · View at Google Scholar · View at Scopus
  26. N. M. Hung, E. Karapınar, and N. V. Luong, “Coupled coincidence point theorem for O-compatible mappings via implicit relation,” Abstract and Applied Analysis, vol. 2012, Article ID 796964, 14 pages, 2012. View at Publisher · View at Google Scholar
  27. D. W. Boyd and J. S. W. Wong, “On nonlinear contractions,” Proceedings of the American Mathematical Society, vol. 20, pp. 458–464, 1969. View at Publisher · View at Google Scholar
  28. A. Mukherjea, “Contractions and completely continuous mappings,” Nonlinear Analysis, vol. 1, no. 3, pp. 235–247, 1977. View at Google Scholar · View at Scopus
  29. 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 Scopus
  30. 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 Scopus
  31. M. Borcut and V. Berinde, “Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces,” Applied Mathematics and Computation, vol. 218, no. 10, pp. 5929–5936, 2012. View at Publisher · View at Google Scholar · View at Scopus
  32. V. Berinde and M. Borcut, “Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 15, pp. 4889–4897, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. E. Karapınar and N. V. Luong, “Quadruple fixed point theorems for nonlinear contractions,” Computers and Mathematics with Applications, vol. 64, no. 6, pp. 1839–1848, 2012. View at Publisher · View at Google Scholar · View at Scopus
  34. M. Berzig and B. Samet, “An extension of coupled fixed point's concept in higher dimension and applications,” Computers and Mathematics with Applications, vol. 63, no. 8, pp. 1319–1334, 2012. View at Publisher · View at Google Scholar · View at Scopus
  35. S. Wang, “Coincidence point theorems for G-isotone mappings in partially ordered metric spaces,” Fixed Point Theory and Applications, vol. 2013, p. 96, 2013. View at Publisher · View at Google Scholar
  36. B. Samet, E. Karapınar, H. Aydi, and V. C. Rajic, “Discussion on some coupled fixed point theorems,” Fixed Point Theory and Applications, vol. 2013, p. 50, 2013. View at Publisher · View at Google Scholar
  37. 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 Scopus