Journal Menu

- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

Abstract and Applied Analysis

Volume 2012 (2012), Article ID 701910, 18 pages

http://dx.doi.org/10.1155/2012/701910

Research Article

## On Generalized Weakly -Contractive Mappings in Partially Ordered -Metric Spaces

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Received 3 August 2012; Accepted 6 September 2012

Academic Editor: Naseer Shahzad

Copyright © 2012 A. Razani and V. Parvaneh. 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

- 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 · View at Zentralblatt MATH - M. Abbas, T. Nazir, and D. Dorić, “Common fixed point of mappings satisfying $(E,A)$ property in generalized metric spaces,”
*Applied Mathematics and Computation*, vol. 218, no. 14, pp. 7665–7670, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Abbas, T. Nazir, and S. Radenović, “Common fixed point of generalized weakly contractive maps in partially ordered $G$-metric spaces,”
*Applied Mathematics and Computation*, vol. 218, no. 18, pp. 9383–9395, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Abbas, T. Nazir, and S. Radenović, “Some periodic point results in generalized metric spaces,”
*Applied Mathematics and Computation*, vol. 217, no. 8, pp. 4094–4099, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - H. Aydi, W. Shatanawi, and C. Vetro, “On generalized weak $G$-contraction mapping in $G$-metric spaces,”
*Computers & Mathematics with Applications*, vol. 62, no. 11, pp. 4223–4229, 2011. View at Publisher · View at Google Scholar - M. Khandaqji, Sh. Al-Sharif, and M. Al-Khaleel, “Properpty $P$ and some fixed point results on $(\psi ,\phi )$-weakly contractive $G$-metric spaces,”
*International Journal of Mathematics and Mathematical Sciences*, vol. 2012, Article ID 675094, 11 pages, 2012. View at Publisher · View at Google Scholar - Z. Mustafa, M. Khandagji, and W. Shatanawi, “Fixed point results on complete $G$-metric spaces,”
*Studia Scientiarum Mathematicarum Hungarica*, vol. 48, no. 3, pp. 304–319, 2011. View at Publisher · View at Google Scholar - Z. Mustafa and H. Obiedat, “A fixed point theorem of Reich in $G$-metric spaces,”
*CUBO: A Mathematical Journal*, vol. 12, no. 1, pp. 83–93, 2010. View at Google Scholar · View at Zentralblatt MATH - 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 · View at Zentralblatt MATH - 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 · View at Zentralblatt MATH - 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 · View at Zentralblatt MATH - W. Shatanawi, “Fixed point theory for contractive mappings satisfying $\mathrm{\Phi}$-maps in $G$-metric spaces,”
*Fixed Point Theory and Applications*, vol. 2010, Article ID 181650, 9 pages, 2010. View at Publisher · 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 · View at Zentralblatt MATH - N. Tahat, H. Aydi, E. Karapınar, and W. Shatanawi, “Common fixed point for single-valued and multi-valued maps satisfying a generalized contraction in $G$-metric spaces,”
*Fixed Point Theory and Applications*, vol. 2012, article 48, 2012. View at Publisher · 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 · View at Zentralblatt MATH - M. S. Khan, M. Swaleh, and S. Sessa, “Fixed point theorems by altering distances between the points,”
*Bulletin of the Australian Mathematical Society*, vol. 30, no. 1, pp. 1–9, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - B. S. Choudhury, “Unique fixed point theorem for weak C-contractive mappings,”
*Kathmandu University Journal of Science, Engineering and Technology*, vol. 5, no. 1, pp. 6–13, 2009. View at Google Scholar - J. Harjani, B. Lopez, and K. Sadarangani, “Fixed point theorems for weakly $C$-contractive mappings in ordered metric spaces,”
*Computers & Mathematics with Applications*, vol. 61, no. 4, pp. 790–796, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - W. Shatanawi, “Fixed point theorems for nonlinear weakly $C$-contractive mappings in metric spaces,”
*Mathematical and Computer Modelling*, vol. 54, no. 11-12, pp. 2816–2826, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Abbas, T. Nazir, and S. Radenović, “Common fixed points of four maps in partially ordered metric spaces,”
*Applied Mathematics Letters*, vol. 24, no. 9, pp. 1520–1526, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - H. K. Nashine and B. Samet, “Fixed point results for mappings satisfying $(\psi ,\phi )$-weakly contractive condition in partially ordered metric spaces,”
*Nonlinear Analysis*, vol. 74, no. 6, pp. 2201–2209, 2011. View at Publisher · View at Google Scholar - G. Jungck, “Compatible mappings and common fixed points,”
*International Journal of Mathematics and Mathematical Sciences*, vol. 9, no. 4, pp. 771–779, 1986. View at Publisher · View at Google Scholar - 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 - W. Shatanawi and B. Samet, “On $(\psi ,\phi )$-weakly contractive condition in partially ordered metric spaces,”
*Computers & Mathematics with Applications*, vol. 62, no. 8, pp. 3204–3214, 2011. View at Publisher · View at Google Scholar - M. Kumar, “Compatible maps in $G$-metric spaces,”
*International Journal of Mathematical Analysis*, vol. 6, no. 29, pp. 1415–1421, 2012. View at Google Scholar - M. Abbas, V. Parvaneh, and A. Razani, “Periodic point of $T$-Ciric generalized contraction mappings in ordered metric spaces,”
*Georgian Mathematical Journal*. In press. - R. Chugh, T. Kadian, A. Rani, and B. E. Rhoades, “Property $P$ in $G$-metric spaces,”
*Fixed Point Theory and Applications*, vol. 2010, Article ID 401684, 12 pages, 2010. View at Google Scholar · View at Zentralblatt MATH - G. S. Jeong and B. E. Rhoades, “Maps for which $F(T)=F({T}^{n})$,”
*Fixed Point Theory and Applications*, vol. 6, pp. 87–131, 2005. View at Google Scholar