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Abstract and Applied Analysis
Volume 2014, Article ID 985080, 10 pages
http://dx.doi.org/10.1155/2014/985080
Research Article

The Generalized Weaker -Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

1Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, P.O. Box 4087, Jeddah 21491, Saudi Arabia
2Department of Applied Mathematics, National Hsinchu University of Education, Taiwan
3Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey
4Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia

Received 6 February 2014; Accepted 7 May 2014; Published 26 May 2014

Academic Editor: Qamrul Hasan Ansari

Copyright © 2014 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. A. Branciari, “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,” Publicationes Mathematicae Debrecen, vol. 57, no. 1-2, pp. 31–37, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. Samet, “Discussion on: a fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces by A. Branciari,” Publicationes Mathematicae Debrecen, vol. 76, no. 3-4, pp. 493–494, 2010. View at Google Scholar · View at MathSciNet
  3. W. A. Kirk and N. Shahzad, “Generalized metrics and Caristi's theorem,” Fixed Point Theory and Applications, vol. 2013, article 129, 2013. View at Publisher · View at Google Scholar
  4. M. Jleli and B. Samet, “The Kannan's fixed point theorem in a cone rectangular metric space,” Journal of Nonlinear Science and its Applications, vol. 2, no. 3, pp. 161–167, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. B. Samet, C. Vetro, and P. Vetro, “Fixed point theorems for α-ψ-contractive type mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 4, pp. 2154–2165, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. U. Ali and T. Kamran, “On (α*,ψ)-contractive multi-valued mappings,” Fixed Point Theory and Applications, vol. 2013, article 137, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  7. M. Jleli, E. Karapınar, and B. Samet, “Best proximity points for generalized alpha-psi-proximal contractive type mappings,” Journal of Applied Mathematics, vol. 2013, Article ID 534127, 10 pages, 2013. View at Publisher · View at Google Scholar
  8. M. Jleli, E. Karapınar, and B. Samet, “Fixed point results for α-ψλ-contractions on gauge spaces and applications,” Abstract and Applied Analysis, vol. 2013, Article ID 730825, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. E. Karapınar and B. Samet, “Generalized α-ψ contractive type mappings and related fixed point theorems with applications,” Abstract and Applied Analysis, vol. 2012, Article ID 793486, 17 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. B. Mohammadi, S. Rezapour, and N. Shahzad, “Some results on fixed points of α-ψ-Ciric generalized multifunctions,” Fixed Point Theory and Applications, vol. 2013, article 24, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  11. R. M. Bianchini and M. Grandolfi, “Trasformazioni di tipo contrattivo generalizzato in uno spazio metrico,” Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali, vol. 45, pp. 212–216, 1968. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. D. Proinov, “A generalization of the Banach contraction principle with high order of convergence of successive approximations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 8, pp. 2361–2369, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. P. D. Proinov, “New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems,” Journal of Complexity, vol. 26, no. 1, pp. 3–42, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. I. A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca Romania, 2001. View at MathSciNet
  15. W. A. Wilson, “On semi-metric spaces,” The American Journal of Mathematics, vol. 53, no. 2, pp. 361–373, 1931. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. Meir and E. Keeler, “A theorem on contraction mappings,” Journal of Mathematical Analysis and Applications, vol. 28, pp. 326–329, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. A. A. Eldred and P. Veeramani, “Existence and convergence of best proximity points,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1001–1006, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. M. de la Sen, “Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings,” Fixed Point Theory and Applications, vol. 2010, Article ID 572057, 23 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. C. M. Chen and W. Y. Sun, “Periodic points and fixed points for the weaker (ϕ,φ)-contractive mappings in complete generalized metric spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 856974, 7 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. E. Karapınar, “Discussion on α-ψ contractions on generalized metric spaces,” Abstract and Applied Analysis, vol. 2014, Article ID 962784, 7 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  21. H. Aydi, E. Karapınar, and B. Samet, “Fixed points for generalized (alpha, psi)-contractions on generalized metric spaces,” Journal of Inequalities and Applications. In press.