Table of Contents
Journal of Operators
Volume 2014, Article ID 389646, 16 pages
http://dx.doi.org/10.1155/2014/389646
Research Article

Coupled Fixed Point Theorems with New Implicit Relations and an Application

1Department of Mathematics, Andhra University, Visakhapatnam 530 003, India
2Department of Mathematics, Lendi Institute of Engineering and Technology, Vizianagaram 535 005, India

Received 28 June 2014; Accepted 1 October 2014; Published 11 November 2014

Academic Editor: Hagen Neidhardt

Copyright © 2014 G. V. R. Babu and P. D. Sailaja. 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. J. Harjani and K. Sadarangani, “Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1188–1197, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 3403–3410, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. H. K. Nashine and B. Samet, “Fixed point results for mappings satisfying (ψ, φ)-weakly contractive condition in partially ordered metric spaces,” Nonlinear Analysis, vol. 74, pp. 2201–2209, 2011. View at Google Scholar
  4. J. J. Nieto and R. Rodriguez-Lopez, “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
  5. J. J. Nieto and R. Rodríguez-López, “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations,” Acta Mathematica Sinica, vol. 23, no. 12, pp. 2205–2212, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. A. C. Ran and M. C. 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
  7. D. J. Guo and V. Lakshmikantham, “Coupled fixed points of nonlinear operators with applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 11, no. 5, pp. 623–632, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. T. Gnana Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 7, pp. 1379–1393, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. V. Lakshmikantham and L. B. Ciric, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 12, pp. 4341–4349, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. B. S. Choudhury and A. Kundu, “A coupled coincidence point result in partially ordered metric spaces for compatible mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 73, no. 8, pp. 2524–2531, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. N. V. Luong and N. X. Thuan, “Coupled fixed points in partially ordered metric spaces and application,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 3, pp. 983–992, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. I. Altun and H. Simsek, “Some fixed point theorems on ordered metric spaces and application,” Fixed Point Theory and Applications, vol. 2010, Article ID 621469, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  13. V. Popa, “Some fixed point theorems for compatible mappings satisfying an implicit relation,” Demonstratio Mathematica, vol. 32, no. 1, pp. 157–163, 1999. View at Google Scholar · View at MathSciNet
  14. I. Altun and D. Turkoglu, “Some fixed point theorems for weakly compatible multivalued mappings satisfying an implicit relation,” Taiwanese Journal of Mathematics, vol. 22, no. 1, pp. 13–21, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  15. I. Altun and D. Turkoglu, “Some fixed point theorems for weakly compatible mappings satisfying an implicit relation,” Taiwanese Journal of Mathematics, vol. 13, no. 4, pp. 1291–1304, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. M. Imdad, S. Kumar, and M. S. Khan, “Remarks on some fixed point theorems satisfying implicit relations,” Radovi Matematicki, vol. 11, no. 1, pp. 135–143, 2002. View at Google Scholar · View at MathSciNet
  17. V. Popa, “A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation,” Demonstratio Mathematica, vol. 33, no. 1, pp. 159–164, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. V. Popa and M. Mocanu, “Altering distance and common fixed points under implicit relations,” Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, pp. 329–337, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. S. Sharma and B. Deshpande, “On compatible mappings satisfying an implicit relation in common fixed point consideration,” Tamkang Journal of Mathematics, vol. 33, no. 3, pp. 245–252, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. D. Turkoglu and I. Altun, “A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying an implicit relation,” Sociedad Matematica Mexicana Boletin, vol. 13, no. 1, pp. 195–205, 2007. View at Google Scholar · View at MathSciNet · View at Scopus