Journal of Applied Mathematics

Volume 2012, Article ID 314279, 10 pages

http://dx.doi.org/10.1155/2012/314279

Research Article

## Tripled Fixed Point Results in Generalized Metric Spaces

^{1}Institut Supérieur d'Informatique et des Technologies de Communication de Hammam Sousse, Université de Sousse, Route GP1-4011, H. Sousse, Tunisia^{2}Department of Mathematics, Atilim University, İncek, 06836 Ankara, Turkey^{3}Department of Mathematics, Hashemite University, Zarqa, Jordan

Received 5 February 2012; Accepted 16 March 2012

Academic Editor: Rudong Chen

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

- L. Ćirić, M. Abbas, B. Damjanović, and R. Saadati, “Common fuzzy fixed point theorems in ordered metric spaces,”
*Mathematical and Computer Modelling*, vol. 53, no. 9-10, pp. 1737–1741, 2011. View at Publisher · View at Google Scholar - Y. J. Cho, R. Saadati, and S. Wang, “Common fixed point theorems on generalized distance in ordered cone metric spaces,”
*Computers & Mathematics with Applications*, vol. 61, no. 4, pp. 1254–1260, 2011. View at Publisher · View at Google Scholar - R. Saadati, S. M. Vaezpour, and Lj. B. Ćirića, “Generalized distance and some common fixed point theorems,”
*Journal of Computational Analysis and Applications*, vol. 12, no. 1-A, pp. 157–162, 2010. View at Google Scholar - B. C. Dhage, “Generalized metric space and mapping with fixed point,”
*Bulletin of Calcutta Mathematical Society*, vol. 84, pp. 329–336, 1992. View at Google Scholar - B. C. Dhage, “On generalized metric spaces and topological structure. II,”
*Pure and Applied Mathematika Sciences*, vol. 40, no. 1-2, pp. 37–41, 1994. View at Google Scholar - B. C. Dhage, “A common fixed point principle in
*D*-metric spaces,”*Bulletin of the Calcutta Mathematical Society*, vol. 91, no. 6, pp. 475–480, 1999. View at Google Scholar - B. C. Dhage, “Generalized metric spaces and topological structure. I,”
*Annalele Stintifice ale Universitatii Al.I. Cuza*, vol. 46, no. 1, pp. 3–24, 2000. View at Google Scholar - Z. Mustafa and B. Sims, “Some remarks concerning
*D*-metric spaces,” in*Proceedings of the International Conference on Fixed Point Theory and Applications*, pp. 189–198, Yokohama, Japan, 2004. View at Google Scholar - Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,”
*Journal of Nonlinear and Convex Analysis*, vol. 7, no. 2, pp. 289–297, 2006. View at Google Scholar - M. Abbas, A. R. Khan, and T. Nazir, “Coupled common fixed point results in two generalized metric spaces,”
*Applied Mathematics and Computation*, vol. 217, no. 13, pp. 6328–6336, 2011. View at Publisher · View at Google Scholar - M. Abbas and B. E. Rhoades, “Common fixed point results for noncommuting mappings without continuity in generalized metric spaces,”
*Applied Mathematics and Computation*, vol. 215, no. 1, pp. 262–269, 2009. 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 - H. Aydi, W. Shatanawi, and C. Vetro, “On generalized weakly
*G*-contraction mapping in*G*-metric spaces,”*Computers & Mathematics with Applications*, vol. 62, pp. 4222–4229, 2011. View at Google Scholar - H. Aydi, “A fixed point result involving a generalized weakly contractive condition in
*G*-metric spaces,”*Bulletin of Mathematical Analysis and Applications*, vol. 3, no. 4, pp. 180–188, 2011. View at Google Scholar - H. Aydi, W. Shatanawi, and M. Postolache, “Coupled fixed point results for ($\psi ,\varphi $)-weakly contractive mappings in ordered
*G*-metric spaces,”*Computers & Mathematics with Applications*, vol. 63, pp. 298–309, 2012. View at Google Scholar - H. Aydi, “A common fixed point of integral type contraction in generalized metric spaces,”
*Journal of Advanced Mathematical Studies*, vol. 5, no. 1, pp. 111–117, 2012. View at Google Scholar - B. S. Choudhury and P. Maity, “Coupled fixed point results in generalized metric spaces,”
*Mathematical and Computer Modelling*, vol. 54, no. 1-2, pp. 73–79, 2011. View at Publisher · View at Google Scholar - Z. Mustafa,
*A new structure for generalized metric spaces with applications to fixed point theory*, Ph.D. thesis, The University of Newcastle, Callaghan, Australia, 2005. - Z. Mustafa, H. Obiedat, and F. Awawdeh, “Some fixed point theorem for mapping on complete
*G*-metric spaces,”*Fixed Point Theory and Applications*, vol. 2008, Article ID 189870, 12 pages, 2008. View at Google Scholar - Z. Mustafa and B. Sims, “Fixed point theorems for contractive mappings in complete
*G*-metric spaces,”*Fixed Point Theory and Applications*, vol. 2009, Article ID 917175, 10 pages, 2009. View at Google Scholar - Z. Mustafa, W. Shatanawi, and M. Bataineh, “Existence of fixed point results in
*G*-metric spaces,”*International Journal of Mathematics and Mathematical Sciences*, vol. 2009, Article ID 283028, 10 pages, 2009. View at Publisher · View at Google Scholar - R. Saadati, S. M. Vaezpour, P. Vetro, and B. E. Rhoades, “Fixed point theorems in generalized partially ordered
*G*-metric spaces,”*Mathematical and Computer Modelling*, vol. 52, no. 5-6, pp. 797–801, 2010. View at Publisher · View at Google Scholar - W. Shatanawi, “Fixed point theory for contractive mappings satisfying Φ-maps in
*G*-metric spaces,”*Fixed Point Theory and Applications*, vol. 2010, Article ID 181650, 9 pages, 2010. View at Google Scholar - W. Shatanawi, “Some fixed point theorems in ordered
*G*-metric spaces and applications,”*Abstract and Applied Analysis*, vol. 2011, Article ID 126205, 11 pages, 2011. View at Publisher · View at Google Scholar - W. Shatanawi, “Coupled fixed point theorems in generalized metric spaces,”
*Hacettepe Journal of Mathematics and Statistics*, vol. 40, no. 3, pp. 441–447, 2011. View at Google Scholar - N. Tahat, H. Aydi, E. Karapinar, and W. Shatanawi, “Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in
_{G}-metric spaces,”*Fixed Point Theory and Applications*, vol. 2012, 48 pages, 2012. 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 A*, vol. 74, no. 15, pp. 4889–4897, 2011. View at Publisher · View at Google Scholar - V. Berinde and M. Borcut, “Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces,”
*Applied Mathematics & Computation*, vol. 218, no. 10, pp. 5929–5936, 2012. View at Google Scholar - 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 - J. Matkowski, “Fixed point theorems for mappings with a contractive iterate at a point,”
*Proceedings of the American Mathematical Society*, vol. 62, no. 2, pp. 344–348, 1977. View at Google Scholar