Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 793486, 17 pages
http://dx.doi.org/10.1155/2012/793486
Research Article

Generalized 𝜶 - 𝝍 Contractive Type Mappings and Related Fixed Point Theorems with Applications

1Department of Mathematics, Atilim University, İncek, 06836 Ankara, Turkey
2Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia

Received 28 May 2012; Accepted 25 July 2012

Academic Editor: Jean Michel Combes

Copyright © 2012 Erdal Karapınar and Bessem Samet. 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. B. Samet, C. Vetro, and P. Vetro, “Fixed point theorems for α-ψ contractive type mappings,” Nonlinear Analysis. Theory, Methods and Applications A, vol. 75, no. 4, pp. 2154–2165, 2012. View at Publisher · View at Google Scholar
  2. V. Berinde, Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, Romania, 2002.
  3. L. B. \'Cirić, “Fixed points for generalized multi-valued contractions,” Matematički Vesnik, vol. 9, no. 24, pp. 265–272, 1972. View at Google Scholar · View at Zentralblatt MATH
  4. 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 Google Scholar · View at Zentralblatt MATH
  5. 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
  6. R. Kannan, “Some results on fixed points,” Bulletin of the Calcutta Mathematical Society, vol. 10, pp. 71–76, 1968. View at Google Scholar
  7. 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
  8. M. Turinici, “Abstract comparison principles and multivariable Gronwall-Bellman inequalities,” Journal of Mathematical Analysis and Applications, vol. 117, no. 1, pp. 100–127, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 1435–1443, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan, “Generalized contractions in partially ordered metric spaces,” Applicable Analysis, vol. 87, no. 1, pp. 109–116, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. I. Altun and H. Simsek, “Some fixed point theorems on ordered metric spaces and application,” Fixed Point Theory and Applications, vol. 2010, Article ID 621469, 17 pages, 2010. View at Google Scholar · View at Zentralblatt MATH
  12. L. Ćirić, N. Cakić, M. Rajović, and J. S. Ume, “Monotone generalized nonlinear contractions in partially ordered metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 131294, 11 pages, 2008. View at Google Scholar · View at Zentralblatt MATH
  13. J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis. Theory, Methods and Applications A, vol. 71, no. 7-8, pp. 3403–3410, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. Petruşel and I. A. Rus, “Fixed point theorems in ordered L-spaces,” Proceedings of the American Mathematical Society, vol. 134, no. 2, pp. 411–418, 2006. View at Publisher · View at Google Scholar
  15. B. Samet, “Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces,” Nonlinear Analysis. Theory, Methods and Applications A, vol. 72, no. 12, pp. 4508–4517, 2010. View at Publisher · View at Google Scholar
  16. J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. W. A. Kirk, P. S. Srinivasan, and P. Veeramani, “Fixed points for mappings satisfying cyclical contractive conditions,” Fixed Point Theory, vol. 4, no. 1, pp. 79–89, 2003. View at Google Scholar · View at Zentralblatt MATH
  18. R. P. Agarwal, M. A. Alghamdi, and N. Shahzad, “Fixed point theory for cyclic generalized contractions in partial metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 40, 2012. View at Publisher · View at Google Scholar
  19. E. Karapınar, “Fixed point theory for cyclic weak ϕ-contraction,” Applied Mathematics Letters, vol. 24, no. 6, pp. 822–825, 2011. View at Publisher · View at Google Scholar
  20. E. Karapınar and K. Sadaranagni, “Fixed point theory for cyclic (ϕ-ψ)-contractions,” Fixed Point Theory and Applications, vol. 2011, article 69, 2011. View at Google Scholar
  21. M. Păcurar and I. A. Rus, “Fixed point theory for cyclic φ-contractions,” Nonlinear Analysis. Theory, Methods and Applications A, vol. 72, no. 3-4, pp. 1181–1187, 2010. View at Publisher · View at Google Scholar
  22. M. A. Petric, “Some results concerning cyclical contractive mappings,” General Mathematics, vol. 18, no. 4, pp. 213–226, 2010. View at Google Scholar
  23. I. A. Rus, “Cyclic representations and fixed points,” Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, vol. 3, pp. 171–178, 2005. View at Google Scholar