Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 621614, 6 pages
http://dx.doi.org/10.1155/2013/621614
Research Article

Fixed Points of Multivalued Nonself Almost Contractions

1Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, P.O. Box 4087, Jeddah 21491, Saudi Arabia
2Department of Mathematics and Computer Science, North University of Baia Mare, Baia Mare, Romania
3Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21859, Saudi Arabia

Received 29 March 2013; Accepted 20 May 2013

Academic Editor: Wei-Shih Du

Copyright © 2013 Maryam A. Alghamdi 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., “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, pp. 475–488, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. N. A. Assad and W. A. Kirk, “Fixed point theorems for set-valued mappings of contractive type,” Pacific Journal of Mathematics, vol. 43, pp. 553–562, 1972. View at Publisher · View at Google Scholar · View at MathSciNet
  3. L. B. Ćirić, “A remark on Rhoades' fixed point theorem for non-self mappings,” International Journal of Mathematics and Mathematical Sciences, vol. 16, no. 2, pp. 397–400, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. N. A. Assad, “On some nonself nonlinear contractions,” Mathematica Japonica, vol. 33, no. 1, pp. 17–26, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. N. A. Assad, “On some nonself mappings in Banach spaces,” Mathematica Japonica, vol. 33, no. 4, pp. 501–515, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. N. A. Assad, “A fixed point theorem in Banach space,” Institut Mathématique. Nouvelle Série, vol. 47, no. 61, pp. 137–140, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. N. A. Assad, “A fixed point theorem for some non-self-mappings,” Tamkang Journal of Mathematics, vol. 21, no. 4, pp. 387–393, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. A. Alghamdi, V. Berinde, and N. Shahzad, “Fixed points of non-self almost contractions,” Carpathian Journal of Mathematics, 2014, In press. View at Google Scholar
  9. M. Berinde and V. Berinde, “On a general class of multi-valued weakly Picard mappings,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 772–782, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. V. Berinde, “Stability of Picard iteration for contractive mappings satisfying an implicit relation,” Carpathian Journal of Mathematics, vol. 27, no. 1, pp. 13–23, 2011. View at Google Scholar · View at MathSciNet
  11. V. Berinde, “On the approximation of fixed points of weak contractive mappings,” Carpathian Journal of Mathematics, vol. 19, no. 1, pp. 7–22, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. V. Berinde, “Approximating fixed points of weak contractions using the Picard iteration,” Nonlinear Analysis Forum, vol. 9, no. 1, pp. 43–53, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. V. Berinde, Iterative Approximation of Fixed Points, vol. 1912 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2nd edition, 2007. View at MathSciNet
  14. V. Berinde and M. Pacurar, “Fixed point theorems for nonself single-valued almost contractions,” Fixed Point Theory. In press. View at Google Scholar
  15. F. Bojor, “Fixed points of Bianchini mappings in metric spaces endowed with a graph,” Carpathian Journal of Mathematics, vol. 28, no. 2, pp. 207–214, 2012. View at Google Scholar
  16. M. Borcut, “Tripled fixed point theorems for monotone mappings in partially ordered metric spaces,” Carpathian Journal of Mathematics, vol. 28, no. 2, pp. 215–222, 2012. View at Google Scholar
  17. J. Caristi, “Fixed point theorems for mappings satisfying inwardness conditions,” Transactions of the American Mathematical Society, vol. 215, pp. 241–251, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Lj. B. Ćirić, J. S. Ume, M. S. Khan, and H. K. Pathak, “On some nonself mappings,” Mathematische Nachrichten, vol. 251, pp. 28–33, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Y. Enjouji, M. Nakanishi, and T. Suzuki, “A generalization of Kannan's fixed point theorem,” Fixed Point Theory and Applications, vol. 2009, Article ID 192872, 10 pages, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. R. H. Haghi, Sh. Rezapour, and N. Shahzad, “On fixed points of quasi-contraction type multifunctions,” Applied Mathematics Letters, vol. 25, no. 5, pp. 843–846, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. S. Khan, M. Swaleh, and S. Sessa, “Fixed point theorems by altering distances between the points,” Bulletin of the Australian Mathematical Society, vol. 30, no. 1, pp. 1–9, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. M. Kikkawa and T. Suzuki, “Some similarity between contractions and Kannan mappings,” Fixed Point Theory and Applications, vol. 2008, Article ID 649749, 8 pages, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. T. A. Lazăr, A. Petruşel, and N. Shahzad, “Fixed points for non-self operators and domain invariance theorems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 1, pp. 117–125, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. M. Nakanishi and T. Suzuki, “An observation on Kannan mappings,” Central European Journal of Mathematics, vol. 8, no. 1, pp. 170–178, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. Păcurar, “Common fixed points for almost Presić type operators,” Carpathian Journal of Mathematics, vol. 28, no. 1, pp. 117–126, 2012. View at Google Scholar · View at MathSciNet
  26. H. K. Pathak and N. Shahzad, “Fixed point results for set-valued contractions by altering distances in complete metric spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 7, pp. 2634–2641, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. H. K. Pathak and N. Shahzad, “Fixed points for generalized contractions and applications to control theory,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 8, pp. 2181–2193, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. S. Reich, “Kannan's fixed point theorem,” Bollettino della Unione Matematica Italiana, vol. 4, pp. 1–11, 1971. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. B. E. Rhoades, “A fixed point theorem for some non-self-mappings,” Mathematica Japonica, vol. 23, no. 4, pp. 457–459, 1978/79. View at Google Scholar · View at MathSciNet
  30. I. A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, Romania, 2001. View at MathSciNet
  31. I. A. Rus, “Properties of the solutions of those equations for which the Krasnoselskii iteration converges,” Carpathian Journal of Mathematics, vol. 28, no. 2, pp. 329–336, 2012. View at Google Scholar
  32. N. Shioji, T. Suzuki, and W. Takahashi, “Contractive mappings, Kannan mappings and metric completeness,” Proceedings of the American Mathematical Society, vol. 126, no. 10, pp. 3117–3124, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. K. Włodarczyk and R. Plebaniak, “Kannan-type contractions and fixed points in uniform spaces,” Fixed Point Theory and Applications, vol. 2011, article 90, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  34. K. Włodarczyk and R. Plebaniak, “Generalized uniform spaces, uniformly locally contractive set-valued dynamic systems and fixed points,” Fixed Point Theory and Applications, vol. 2012, article 104, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  35. K. Włodarczyk and R. Plebaniak, “Leader type contractions, periodic and fixed points and new completivity in quasi-gauge spaces with generalized quasi-pseudodistances,” Topology and its Applications, vol. 159, no. 16, pp. 3504–3512, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. K. Włodarczyk and R. Plebaniak, “Contractivity of Leader type and fixed points in uniform spaces with generalized pseudodistances,” Journal of Mathematical Analysis and Applications, vol. 387, no. 2, pp. 533–541, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  37. K. Włodarczyk and R. Plebaniak, “Contractions of Banach, Tarafdar, Meir- Keller, Ciric-Jachymski-Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances,” Journal of Mathematical Analysis and Applications, vol. 404, no. 2, pp. 338–350, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  38. F. Khojasteh and V. Rakočević, “Some new common fixed point results for generalized contractive multi-valued non-self-mappings,” Applied Mathematics Letters, vol. 25, no. 3, pp. 287–293, 2012. View at Publisher · View at Google Scholar
  39. B. E. Rhoades, “A comparison of various definitions of contractive mappings,” Transactions of the American Mathematical Society, vol. 226, pp. 257–290, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  40. R. Kannan, “Some results on fixed points,” Bulletin of the Calcutta Mathematical Society, vol. 60, pp. 71–76, 1968. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  41. S. K. Chatterjea, “Fixed-point theorems,” Doklady Bolgarskoĭ Akademii Nauk. Comptes Rendus de l'Académie Bulgare des Sciences, vol. 25, pp. 727–730, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  42. T. Zamfirescu, “Fix point theorems in metric spaces,” Archiv der Mathematik, vol. 23, pp. 292–298, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  43. M. Turinici, “Weakly contractive maps in altering metric spaces,” http://arxiv.org/abs/1302.4013. View at Google Scholar