ISRN Applied Mathematics

Volume 2012, Article ID 539125, 16 pages

http://dx.doi.org/10.5402/2012/539125

Research Article

## Quadruple Fixed Point Theorems in Partially Ordered Metric Spaces Depending on Another Function

^{1}Université de Sousse Institut Supérieur d'Informatique et des Technologies de Communication de Hammam Sousse, Route GP1, H. Sousse 4011, Tunisia^{2}Department of Mathematics, Atılım University, 06836 İncek, Ankara, Turkey

Received 27 February 2012; Accepted 30 April 2012

Academic Editor: G. Wang

Copyright © 2012 Hassen Aydi 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

- E. S. Wolk, “Continuous convergence in partially ordered sets,”
*General Topology and its Applications*, vol. 5, no. 3, pp. 221–234, 1975. View at Google Scholar · View at Zentralblatt MATH - B. Monjardet, “Metrics on partially ordered sets—a survey,”
*Discrete Mathematics*, vol. 35, pp. 173–184, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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 - 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 - 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 - H. Aydi, “Coincidence and common fixed point results for contraction type maps in partially ordered metric spaces,”
*International Journal of Mathematical Analysis*, vol. 5, no. 13– 16, pp. 631–642, 2011. View at Google Scholar - H. K. Nashine and B. Samet, “Fixed point results for mappings satisfying $(\psi ,\phi )$-weakly contractive condition in partially ordered metric spaces,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 74, no. 6, pp. 2201–2209, 2011. View at Publisher · View at Google Scholar - T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 65, no. 7, pp. 1379–1393, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - V. Lakshmikantham and L. Ćirić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 70, no. 12, pp. 4341–4349, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Abbas, M. Ali Khan, and S. Radenović, “Common coupled fixed point theorems in cone metric spaces for $w$-compatible mappings,”
*Applied Mathematics and Computation*, vol. 217, no. 1, pp. 195–202, 2010. View at Publisher · View at Google Scholar - H. Aydi, “Some coupled fixed point results on partial metric spaces,”
*International Journal of Mathematics and Mathematical Sciences*, vol. 2011, Article ID 647091, 11 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - H. Aydi, B. Samet, and C. Vetro, “Coupled fixed point results in cone metric spaces for $\&x7e;w$-compatible mappings,”
*Fixed Point Theory and Applications*, vol. 2011, article 27, 2011. View at Google Scholar - H. Aydi, E. Karapınar, and W. Shatanawi, “Coupled fixed point results for $(\psi ,\phi )$-weakly contractive condition in ordered partial metric spaces,”
*Computers & Mathematics with Applications*, vol. 62, no. 12, pp. 4449–4460, 2011. View at Publisher · View at Google Scholar - H. Aydi, M. Postolache, and W. Shatanawi, “Coupled fixed point results for $(\psi ,\phi )$-weakly contractive mappings in ordered $G$-metric spaces,”
*Computers & Mathematics with Applications*, vol. 63, no. 1, pp. 298–309, 2012. View at Publisher · View at Google Scholar - H. Aydi, B. Damjanović, B. Samet, and W. Shatanawi, “Coupled fixed point theorems for nonlinear contractions in partially ordered $G$-metric spaces,”
*Mathematical and Computer Modelling*, vol. 54, no. 9-10, pp. 2443–2450, 2011. View at Publisher · View at Google Scholar - B. S. Choudhury, N. Metiya, and A. Kundu, “Coupled coincidence point theorems in ordered metric spaces,”
*Annali dell'Universitá di Ferrara*, vol. 57, no. 1, pp. 1–16, 2011. View at Publisher · View at Google Scholar - E. Karapınar, “Couple fixed point on cone metric spaces,”
*Gazi University Journal of Science*, vol. 24, no. 1, pp. 51–58, 2011. View at Google Scholar - E. Karapınar, “Couple fixed point theorems for nonlinear contractions in cone metric spaces,”
*Computers & Mathematics with Applications*, vol. 59, no. 12, pp. 3656–3668, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - N. V. Luong and N. X. Thuan, “Coupled fixed points in partially ordered metric spaces and application,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 74, no. 3, pp. 983–992, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - B. Samet, “Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 72, no. 12, pp. 4508–4517, 2010. View at Publisher · View at Google Scholar - V. Berinde and M. Borcut, “Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 74, no. 15, pp. 4889–4897, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - B. Samet and C. Vetro, “Coupled fixed point, $f$-invariant set and fixed point of $N$-order,”
*Annals of Functional Analysis*, vol. 1, no. 2, pp. 46–56, 2010. View at Google Scholar - E. Karapınar, “Quartet fixed point for nonlinear contraction,” http://arxiv.org/abs/1106.5472.
- E. Karapınar and N. V. Luong, “Quadruple fixed point theorems for nonlinear contractions,”
*Computers & Mathematics with Applications*, vol. 64, pp. 1839–1848, 2012. View at Publisher · View at Google Scholar - E. Karapınar, “Quadruple fixed point theorems for weak $\phi $-contractions,”
*ISRN Mathematical Analysis*, vol. 2011, Article ID 989423, 15 pages, 2011. View at Google Scholar - E. Karapınar and V. Berinde, “Quadruple fixed point theorems for nonlinear contractions in partially ordered metric spaces,”
*Banach Journal of Mathematical Analysis*, vol. 6, no. 1, pp. 74–89, 2012. View at Google Scholar - E. Karapınar, “A new quartet fixed point theorem for nonlinear contractions,”
*Journal of Fixed Point Theory Appli*, vol. 6, no. 2, pp. 119–135, 2011. View at Google Scholar - 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 - 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 - 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 - N. V. Luong and N. X. Thuan, “Coupled fixed point theorems in partially ordered metric spaces,”
*Bulletin of Mathematical Analysis and Applications*, vol. 2, no. 4, pp. 16–24, 2010. View at Google Scholar