Table of Contents
Journal of Operators
Volume 2013, Article ID 813707, 6 pages
http://dx.doi.org/10.1155/2013/813707
Research Article

Some Common Fixed Point Results for Rational Type Contraction Mappings in Complex Valued Metric Spaces

1Department of Mathematics, Khalsa College of Engineering & Technology (Punjab Technical University), Ranjit Avenue, Amritsar 143001, India
2Department of Mathematics, Lovely Professional University, Phagwara 144411, India

Received 21 March 2013; Accepted 8 May 2013

Academic Editor: Ram U. Verma

Copyright © 2013 Sumit Chandok and Deepak Kumar. 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 MathSciNet
  2. G. V. R. Babu and P. Subhashini, “Coupled common fixed point theorems of Ciric type g-weak contractions with CLRg-property,” Journal of Nonlinear Analysis and Optimization: Theory and Applications. In press.
  3. S. Bhatt, S. Chaukiyal, and R. C. Dimri, “A common fixed point theorem for weakly compatible maps in complex valued metric spaces,” International Journal of Mathematical Sciences & Applications, vol. 1, no. 3, pp. 1385–1389, 2011. View at Google Scholar · View at MathSciNet
  4. S. Chandok, “Some common fixed point theorems for generalized nonlinear contractive mappings,” Computers & Mathematics with Applications, vol. 62, no. 10, pp. 3692–3699, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  5. S. Chandok, “Common fixed points, invariant approximation and generalized weak contractions,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 102980, 11 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. Chandok, “Some common fixed point theorems for Ciric type contraction mapping,” Tamkang Journal of Mathematics, vol. 43, no. 2, pp. 187–202, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. S. Chandok, “Common fixed points for generalized nonlinear contractive mappings in metric spaces,” Matematichki Vesnik, vol. 65, no. 1, pp. 29–34, 2013. View at Google Scholar · View at MathSciNet
  8. S. Chandok, “Some common fixed point theorems for a pair of different compatible type mappings,” Annales Ordea University-Matematică Fascicola, vol. 20, no. 2, 2013. View at Google Scholar
  9. S. Chandok, “Some common fixed point results for generalized weak contractive mappings in partially ordered metric spaces,” Journal of Nonlinear Analysis and Optimization: Theory and Applications, vol. 4, no. 1, pp. 45–52, 2013. View at Google Scholar
  10. S. Chandok, M. S. Khan, and K. P. R. Rao, “Some coupled common fixed point theorems for a pair of mappings satisfying a contractive condition of rational type without monotonicity,” International Journal of Mathematical Analysis, vol. 7, no. 9–12, pp. 433–440, 2013. View at Google Scholar · View at MathSciNet
  11. S. Chandok and J. K. Kim, “Fixed point theorem in ordered metric spaces for generalized contractions mappings satisfying rational type expressions,” Journal of Nonlinear Functional Analysis and Application, vol. 17, no. 3, pp. 301–306, 2012. View at Google Scholar
  12. S. Chandok, J. Liang, and D. O'Regan, “Common fixed points and invariant approximations for noncommuting contraction mappings in strongly convex metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 14, 2013. View at Google Scholar
  13. S. Chandok, Z. Mustafa, and M. Postolache, “Coupled common fixed point theorems for mixed g-monotone mappings in partially ordered G-metric spaces,” UPB Scientific Bulletin A. In press.
  14. S. Chandok, T. D. Narang, and M. A. Taoudi, “Some common fixed point results in partially ordered metric spaces for generalized rational type contraction mappings,” Vietnam Journal of Mathematics. View at Publisher · View at Google Scholar
  15. S. Chauhan, W. Sintunavarat, and P. Kumam, “Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using (JCLR)-property,” Applied Mathematics, vol. 3, no. 9, pp. 976–982, 2012. View at Publisher · View at Google Scholar
  16. S. Chauhan, “Fixed points of weakly compatible mappings in fuzzy metric spaces satisfying common limit in the range property,” Indian Journal of Mathematics, vol. 54, no. 3, pp. 375–397, 2012. View at Google Scholar
  17. S. Chauhan, S. Bhatnagar, and S. Radenovic, “Common fixed point theorems for weakly compatible mappings infuzzy metric spaces,” Le Matematiche. In press.
  18. S. D. Diwan and R. Gupta, “A common fixed point theorem for Gregus type mappings,” Thai Journal of Mathematics. In press.
  19. M. Imdad, B. D. Pant, and S. Chauhan, “Fixed point theorems in Menger spaces using the CLRST property and applications,” Journal of Nonlinear Analysis and Optimization, vol. 3, no. 2, pp. 225–237, 2012. View at Google Scholar · View at MathSciNet
  20. M. Jain, K. Tas, S. Kumar, and N. Gupta, “Coupled fixed point theorems for a pair of weakly compatible maps along with CLRg-property in fuzzy metric spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 961210, 13 pages, 2012. View at Google Scholar · View at MathSciNet
  21. M. Jain and S. Kumar, “A common fixed point theorem in fuzzy metric space using the property (CLRg),” Thai Journal of Mathematics. In press.
  22. G. Jungck, “Compatible mappings and common fixed points,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 4, pp. 771–779, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  23. G. Jungck, “Compatible mappings and common fixed points. II,” International Journal of Mathematics and Mathematical Sciences, vol. 11, no. 2, pp. 285–288, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  24. G. Jungck, “Common fixed points for commuting and compatible maps on compacta,” Proceedings of the American Mathematical Society, vol. 103, no. 3, pp. 977–983, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  25. G. Jungck and B. E. Rhoades, “Fixed point theorems for occasionally weakly compatible mappings,” Fixed Point Theory, vol. 7, no. 2, pp. 287–296, 2006. View at Google Scholar · View at MathSciNet
  26. M. Kumar, P. Kumar, and S. Kumar, “Some common fixed point theorems using (CLRg)-property in cone metric spaces,” Advances Fixed Point Theory, vol. 2, no. 3, pp. 340–356, 2012. View at Google Scholar
  27. H. K. Pathak, R. Rodríguez-López, and R. K. Verma, “A common fixed point theorem of integral type using implicit relation,” Nonlinear Functional Analysis and Applications, vol. 15, no. 1, pp. 1–12, 2010. View at Google Scholar · View at MathSciNet
  28. S. Sessa, “On a weak commutativity condition of mappings in fixed point considerations,” Institut Mathématique. Publications, vol. 32, no. 46, pp. 149–153, 1982. View at Google Scholar · View at MathSciNet
  29. 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
  30. 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
  31. W. Sintunavarat and P. Kumam, “Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces,” Journal of Applied Mathematics, vol. 2011, Article ID 637958, 14 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  32. 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
  33. W. Sintunavarat and P. Kumam, “Common fixed points for R-weakly commuting in fuzzy metric spaces,” Annali dell'Universitá di Ferrara, vol. 58, no. 2, pp. 389–406, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  34. 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 Google Scholar
  35. R. K. Verma and H. K. Pathak, “Common fixed point theorems using property (E.A) in complex-vauled metric spaces,” Thai Journal of Mathematics. In press.