Table of Contents Author Guidelines Submit a Manuscript
Table of Contents Alerts

To receive news and publication updates for The Scientific World Journal, enter your email address in the box below.

The Scientific World Journal
Volume 2014 (2014), Article ID 860436, 6 pages
http://dx.doi.org/10.1155/2014/860436
Research Article

A Hybrid Common Fixed Point Theorem under Certain Recent Properties

Zoran Kadelburg,1 Sunny Chauhan,2 and Mohammad Imdad3

1Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Beograd, Serbia
2R. H. Government Postgraduate College, Kashipur, Uttarakhand 244713, India
3Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India

Received 30 August 2013; Accepted 24 November 2013; Published 23 January 2014

Academic Editors: V. Ravichandran and X. Song

Copyright © 2014 Zoran Kadelburg 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. S. B. Nadler Jr., “Multivalued contraction mappings,” Pacific Journal of Mathematics, vol. 20, no. 2, pp. 457–488, 1969. View at Google Scholar
  2. B. Fisher, “Common fixed point theorems for mappings and set-valued mappings,” Rostocker Mathematisches Kolloquium, vol. 18, pp. 69–77, 1981. View at Google Scholar
  3. T. Hu, “Fixed point theorems for multivalued mappings,” Canadian Mathematical Bulletin, vol. 23, pp. 193–197, 1980. View at Google Scholar
  4. M. Imdad, M. S. Khan, and S. Sessa, “On some weak conditions of commutativity in common fixed point theorems,” International Journal of Mathematics and Mathematical Sciences, vol. 11, no. 2, pp. 289–296, 1988. View at Google Scholar
  5. T. Kubiak, “Fixed point theorems for contractive type multivalued mappings,” Mathematica Japonica, vol. 30, no. 1, pp. 89–101, 1985. View at Google Scholar
  6. S. A. Naimpally, S. L. Singh, and J. H. M. Whitfield, “Coincidence theorems for hybrid contractions,” Mathematische Nachrichten, vol. 127, pp. 177–180, 1986. View at Google Scholar
  7. S. Sessa, M. S. Khan, and M. Imdad, “Common fixed point theorem with a weak commutativity condition,” Glasnik Matematicki, vol. 21, no. 41, pp. 225–235, 1986. View at Google Scholar
  8. H. Kaneko, “Single-valued and multi-valued f-contractions,” Bollettino della Unione Matematica Italiana A, vol. 4, pp. 29–33, 1985. View at Google Scholar
  9. H. Kaneko, “A common fixed point of weakly commuting multi-valued mappings,” Mathematica Japonica, vol. 33, no. 5, pp. 741–744, 1988. View at Google Scholar
  10. S. L. Singh, K. S. Ha, and Y. J. Cho, “Coincidence and fixed points of nonlinear hybrid contractions,” International Journal of Mathematics and Mathematical Sciences, vol. 12, no. 2, pp. 247–256, 1989. View at Google Scholar
  11. H. K. Pathak, “Fixed point theorems for weak compatible multi-valued and single-valued mappings,” Acta Mathematica Hungarica, vol. 67, no. 1-2, pp. 69–78, 1995. View at Publisher · View at Google Scholar · View at Scopus
  12. J. Ali and M. Imdad, “Common fixed points of nonlinear hybrid mappings under strict contractions in semi-metric spaces,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 4, pp. 830–837, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Dhompongsa and H. Yingtaweesittikul, “Fixed points for multivalued mappings and the metric completeness,” Fixed Point Theory and Applications, vol. 2009, Article ID 972395, 15 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Imdad, A. Ahmad, and S. Kumar, “On nonlinear nonself hybrid contractions,” Radovi Matematicki, vol. 10, no. 2, pp. 233–244, 2001. View at Google Scholar
  15. M. Imdad and A. H. Soliman, “Some common fixed point theorems for a pair of tangential mappings in symmetric spaces,” Applied Mathematics Letters, vol. 23, no. 4, pp. 351–355, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. H. Kaneko and S. Sessa, “Fixed point theorems for compatible multi-valued and single-valued mappings,” International Journal of Mathematics and Mathematical Sciences, vol. 12, no. 2, pp. 257–262, 1989. View at Google Scholar
  17. H. K. Pathak, S. M. Kang, and Y. J. Cho, “Coincidence and fixed point theorems for nonlinear hybrid generalized contractions,” Czechoslovak Mathematical Journal, vol. 48, no. 2, pp. 341–357, 1998. View at Publisher · View at Google Scholar · View at Scopus
  18. H. K. Pathak and M. S. Khan, “Fixed and coincidence points of hybrid mappings,” Archiv der Mathematik, vol. 38, pp. 201–208, 2002. View at Google Scholar
  19. S. L. Singh and A. M. Hashim, “New coincidence and fixed point theorems for strictly contractive hybrid maps,” Australian Journal of Mathematical Analysis and Applications, vol. 2, article 12, no. 1, 7 pages, 2005. View at Google Scholar
  20. S. L. Singh and S. N. Mishra, “Coincidences and fixed points of nonself hybrid contractions,” Journal of Mathematical Analysis and Applications, vol. 256, no. 2, pp. 486–497, 2001. View at Publisher · View at Google Scholar · View at Scopus
  21. S. L. Singh and S. N. Mishra, “Coincidence theorems for certain classes of hybrid contractions,” Fixed Point Theory and Applications, vol. 2010, Article ID 898109, 14 pages, 2010. View at Publisher · View at Google Scholar
  22. G. Jungck and B. E. Rhoades, “Fixed points for set valued functions without continuity,” Indian Journal of Pure and Applied Mathematics, vol. 29, no. 3, pp. 227–238, 1998. View at Google Scholar · View at Scopus
  23. M. Abbas and B. E. Rhoades, “Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type,” Fixed Point Theory and Applications, vol. 2007, Article ID 54101, 9 pages, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. H. K. Pathak and R. Rodriguez-Lopez, “Noncommutativity of mappings in hybrid fixed point results,” Boundary Value Problems, vol. 2013, article 145, 21 pages, 2013. View at Google Scholar
  25. D. -Doric, Z. Kadelburg, and S. Radenovic, “A note on occasionally weakly compatible mappings and common fixed points,” Fixed Point Theory, vol. 13, no. 2, pp. 475–480, 2012. View at Google Scholar
  26. M. Aamri and D. El Moutawakil, “Some new common fixed point theorems under strict contractive conditions,” Journal of Mathematical Analysis and Applications, vol. 270, no. 1, pp. 181–188, 2002. View at Publisher · View at Google Scholar · View at Scopus
  27. T. Kamran, “Coincidence and fixed points for hybrid strict contractions,” Journal of Mathematical Analysis and Applications, vol. 299, no. 1, pp. 235–241, 2004. View at Publisher · View at Google Scholar · View at Scopus
  28. 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 Scopus
  29. M. Imdad, S. Chauhan, A. H. Soliman, and M. A. Ahmed, “Hybrid fixed point theorems in symmetric spaces via common limit range property,” Demonstratio Mathematica. In press.
  30. W. Sintunavarat and P. Kumam, “Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition,” Applied Mathematics Letters, vol. 22, no. 12, pp. 1877–1881, 2009. View at Publisher · View at Google Scholar · View at Scopus