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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 352927, 10 pages
http://dx.doi.org/10.1155/2013/352927
Research Article

Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces

1Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, COMSATS Institute of Information Technology, Chak Shahzad, Islamabad, Pakistan
3Università Degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi 34,90123 Palermo, Italy

Received 11 April 2013; Revised 22 May 2013; Accepted 22 May 2013

Academic Editor: Erdal Karapinar

Copyright © 2013 Marwan Amin Kutbi 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. A. Azam, B. Fisher, and M. Khan, “Common fixed point theorems in complex valued metric spaces,” Numerical Functional Analysis and Optimization, vol. 32, no. 3, pp. 243–253, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. Ahmad, M. Arshad, and C. Vetro, “On a theorem of Khan in a generalized metric space,” International Journal of Analysis, vol. 2013, Article ID 852727, 6 pages, 2013. View at Publisher · View at Google Scholar
  3. M. Arshad, A. Shoaib, and I. Beg, “Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered complete dislocated metric space,” Fixed Point Theory and Applications, vol. 2013, article 115, 2013. View at Publisher · View at Google Scholar
  4. M. Arshad, J. Ahmad, and E. Karapinar, “Some common fixed point results in rectangular metric spaces,” International Journal of Analysis, vol. 2013, Article ID 307234, 7 pages, 2013. View at Publisher · View at Google Scholar
  5. M. Arshad and J. Ahmad, “On multivalued contractions in cone metric spaces without normality,” The Scientific World Journal. In press.
  6. M. Arshad, E. Karapinar, and J. Ahmad, “Some unique fixed point theorem for rational contractions in partially ordered metric spaces,” Journal of Inequalities and Applications, vol. 2013, article 248, 2013. View at Publisher · View at Google Scholar
  7. H. Aydi, E. Karapınar, and W. Shatanawi, “Tripled fixed point results in generalized metric spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 314279, 10 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H. Aydi, E. Karapınar, and C. Vetro, “Meir-Keeler type contractions for tripled fixed points,” Acta Mathematica Scientia B, vol. 32, no. 6, pp. 2119–2130, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. H. Aydi, B. Samet, and C. Vetro, “Coupled fixed point results in cone metric spaces for ω~-compatible mappings,” Fixed Point Theory and Applications, vol. 2011, article 27, 15 pages, 2011. View at MathSciNet
  10. A. Azam and M. Arshad, “Common fixed points of generalized contractive maps in cone metric spaces,” Iranian Mathematical Society, vol. 35, no. 2, pp. 255–264, 2009. View at Zentralblatt MATH · View at MathSciNet
  11. C. di Bari and P. Vetro, “φ-pairs and common fixed points in cone metric spaces,” Rendiconti del Circolo Matematico di Palermo Series 2, vol. 57, no. 2, pp. 279–285, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. C. di Bari and P. Vetro, “Weakly φ-pairs and common fixed points in cone metric spaces,” Rendiconti del Circolo Matematico di Palermo Series 2, vol. 58, no. 1, pp. 125–132, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. Bhatt, S. Chaukiyal, and R. C. Dimri, “Common fixed point of mappings satisfying rational inequality in complex valued metric space,” International Journal of Pure and Applied Mathematics, vol. 73, no. 2, pp. 159–164, 2011. View at Zentralblatt MATH · View at MathSciNet
  14. N. Hussain, M. A. Khamsi, and A. Latif, “Banach operator pairs and common fixed points in hyperconvex metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 17, pp. 5956–5961, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. A. Kutbi, J. Ahmad, N. Hussain, and M. Arshad, “Common fixed point results for mappings with rational expressions,” Abstract and Applied Analysis. In press. View at Publisher · View at Google Scholar
  16. E. Karapınar, “Some nonunique fixed point theorems of Ćirić type on cone metric spaces,” Abstract and Applied Analysis, vol. 2010, Article ID 123094, 14 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. E. Karapınar, “Couple fixed point theorems for nonlinear contractions in cone metric spaces,” Computers & Mathematics with Applications, vol. 59, no. 12, pp. 3656–3668, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. C. Mongkolkeha, W. Sintunavarat, and P. Kumam, “Fixed point theorems for contraction mappings in modular metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 93, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  19. F. Rouzkard and M. Imdad, “Some common fixed point theorems on complex valued metric spaces,” Computers & Mathematics with Applications, vol. 64, no. 6, pp. 1866–1874, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. W. Sintunavarat and P. Kumam, “Generalized common fixed point theorems in complex valued metric spaces and applications,” Journal of Inequalities and Applications, vol. 2012, article 84, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. W. Sintunavarat, Y. J. Cho, and P. Kumam, “Urysohn integral equations approach by common fixed points in complex valued metric spaces,” Advances in Difference Equations, vol. 2013, article 49, 2013. View at Publisher · View at Google Scholar
  22. W. Sintunavarat and P. Kumam, “Weak condition for generalized multi-valued (f,α,β)-weak contraction mappings,” Applied Mathematics Letters, vol. 24, no. 4, pp. 460–465, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  23. W. Sintunavarat, Y. J. Cho, and P. Kumam, “Common fixed point theorems for c-distance in ordered cone metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 1969–1978, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  24. W. Sintunavarat and P. Kumam, “Common fixed point theorems for generalized JH-operator classes and invariant approximations,” Journal of Inequalities and Applications, vol. 2011, article 67, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  25. W. Sintunavarat and P. Kumam, “Common fixed points of f-weak contractors in cone metric spaces,” Bulletin of the Iranian Mathematical Society, vol. 38, no. 2, pp. 293–303, 2012. View at MathSciNet
  26. N. Tahat, H. Aydi, E. Karapinar, and W. Shatanawi, “Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 48, 2012. View at Publisher · View at Google Scholar
  27. 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 Zentralblatt MATH · View at MathSciNet
  28. B. Samet, E. Karapinar, H. Aydi, and V. Cojbasic, “Discussion on some coupled fixed point theorems,” Fixed Point Theory and Applications, vol. 2013, article 50, 2013. View at Publisher · View at Google Scholar
  29. B. Samet and C. Vetro, “Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 12, pp. 4260–4268, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet