Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 518734, 9 pages
http://dx.doi.org/10.1155/2012/518734
Research Article

A Generalization of Ćirić Quasicontractions

1Department of Mathematics, Atilim University, İncek, 06836 Ankara, Turkey
2Department of Mathematics, Vinh University, 182 Le Duan, Vinh City, Vietnam

Received 26 October 2011; Accepted 4 December 2011

Academic Editor: Simeon Reich

Copyright © 2012 Erdal Karapınar 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. K. C. Border, Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, New York, NY, USA, 1985. View at Publisher · View at Google Scholar · View at MathSciNet
  2. E. A. Ok, Real Analysis with Economic Applications, Princeton University Press, Princeton, NJ, USA, 2007.
  3. J. W. de Bakker and J. I. Zucker, “Processes and the denotational semantics of concurrency,” Information and Control, vol. 54, no. 1-2, pp. 70–120, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. R. Heckmann, “Approximation of metric spaces by partial metric spaces,” Applied Categorical Structures, vol. 7, no. 1-2, pp. 71–83, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. G. Matthews, “Partial metric topology,” Research Report 212, Department of Computer Science, University of Warwick, 1992. View at Google Scholar
  6. S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations itegrales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922. View at Google Scholar
  7. 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
  8. S. Reich, “Kannan's fixed point theorem,” Bollettino della Unione Matematica Italiana IV, vol. 4, no. 4, pp. 1–11, 1971. View at Google Scholar · View at Zentralblatt MATH
  9. S. Reich, “Some remarks concerning contraction mappings,” Canadian Mathematical Bulletin, vol. 14, pp. 121–124, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. Reich, “Fixed points of contractive functions,” Bollettino della Unione Matematica Italiana IV, vol. 5, pp. 26–42, 1972. View at Google Scholar · View at Zentralblatt MATH
  11. S. K. Chatterjea, “Fixed-point theorems,” Comptes Rendus de l'Académie Bulgare des Sciences, vol. 25, pp. 727–730, 1972. View at Google Scholar · View at Zentralblatt MATH
  12. G. E. Hardy and T. D. Rogers, “A generalization of a fixed point theorem of Reich,” Canadian Mathematical Bulletin, vol. 16, pp. 201–206, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. L. B. Ćirić, “Generalized contraction and fixed point theorems,” Publications de l'Institut Mathématique, vol. 12, no. 26, pp. 19–26, 1971. View at Google Scholar
  14. L. B. Ćirić, “A generalization of Banach's contraction principle,” Proceedings of the American Mathematical Society, vol. 45, pp. 267–273, 1974. View at Google Scholar · View at Zentralblatt MATH
  15. L. \'Cirić, “On contraction type mappings,” Mathematica Balkanica, vol. 1, pp. 52–57, 1971. View at Google Scholar · View at Zentralblatt MATH
  16. M. Edelstein, “On fixed and periodic points under contractive mappings,” Journal of the London Mathematical Society II, vol. 37, pp. 74–79, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. E. Karapınar, “Fixed point theory for cyclic weak ϕ-contraction,” Applied Mathematics Letters. An International Journal of Rapid Publication, vol. 24, no. 6, pp. 822–825, 2011. View at Publisher · View at Google Scholar
  18. E. Karapınar, “Fixed point theorems in cone Banach spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 609281, 9 pages, 2009. View at Google Scholar · View at Zentralblatt MATH
  19. 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
  20. K. P. Chi and H. T. Thuy, “A fixed point theorem in 2-metric spaces for a class of maps that satisfy a contractive condition dependent on an another function,” Lobachevskii Journal of Mathematics, vol. 31, no. 4, pp. 338–346, 2010. View at Publisher · View at Google Scholar
  21. S. Moradi and M. Omid, “A fixed-point theorem for integral type inequality depending on another function,” International Journal of Mathematical Analysis, vol. 4, no. 29–32, pp. 1491–1499, 2010. View at Google Scholar · View at Zentralblatt MATH
  22. K. P. Chi, “On a fixed point theorem for certain class of maps satisfying a contractive condition depended on an another function,” Lobachevskii Journal of Mathematics, vol. 30, no. 4, pp. 289–291, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH