- 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 908423, 15 pages

http://dx.doi.org/10.1155/2012/908423

## Some Fixed and Periodic Points in Abstract Metric Spaces

^{1}School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia^{2}Department of Mathematics, Lahore University of Management Sciences, Lahore 54792, Pakistan^{3}Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Beograd, Serbia^{4}Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia

Received 23 July 2012; Accepted 16 September 2012

Academic Editor: Ngai-Ching Wong

Copyright © 2012 Abd Ghafur Bin Ahmad 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. Kantorovitch, “The method of successive approximations for functional equations,”
*Acta Mathematica*, vol. 71, pp. 63–97, 1939. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - L. V. Kantorovič, “The principle of the majorant and Newton's method,” vol. 76, pp. 17–20, 1951.
- J. S. Vandergraft, “Newton's method for convex operators in partially ordered spaces,”
*SIAM Journal on Numerical Analysis*, vol. 4, pp. 406–432, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - P. P. Zabreĭko, “K-metric and K-normed spaces: survey,”
*Collectanea Mathematica*, vol. 48, pp. 852–859, 1997. - K. Deimling,
*Nonlinear Functional Analysis*, Springer, Berlin, Germany, 1985. - H. Mohebi, “Topical functions and their properties in a class of ordered Banach spaces,” in
*Continuous Optimization, Current Trends and Modern Applications*, vol. 99, pp. 343–361, Springer, New York, NY, USA, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - L.-G. Huang and X. Zhang, “Cone metric spaces and fixed point theorems of contractive mappings,”
*Journal of Mathematical Analysis and Applications*, vol. 332, no. 2, pp. 1468–1476, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Abbas and G. Jungck, “Common fixed point results for noncommuting mappings without continuity in cone metric spaces,”
*Journal of Mathematical Analysis and Applications*, vol. 341, no. 1, pp. 416–420, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Abbas and B. E. Rhoades, “Fixed and periodic point results in cone metric spaces,”
*Applied Mathematics Letters*, vol. 22, no. 4, pp. 511–515, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Abbas, B. E. Rhoades, and T. Nazir, “Common fixed points for four maps in cone metric spaces,”
*Applied Mathematics and Computation*, vol. 216, no. 1, pp. 80–86, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - G. Jungck, S. Radenović, S. Radojević, and V. Rakočević, “Common fixed point theorems for weakly compatible pairs on cone metric spaces,”
*Fixed Point Theory and Applications*, Article ID 643840, 13 pages, 2009. View at Zentralblatt MATH - S. Radenović, “Common fixed points under contractive conditions in cone metric spaces,”
*Computers & Mathematics with Applications*, vol. 58, no. 6, pp. 1273–1278, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - S. Radenović and B. E. Rhoades, “Fixed point theorem for two non-self mappings in cone metric spaces,”
*Computers & Mathematics with Applications*, vol. 57, no. 10, pp. 1701–1707, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - S. Rezapour and R. Hamlbarani, “Some notes on the paper Cone metric spaces and fixed point theorems of contractive mappings,”
*Journal of Mathematical Analysis and Applications*, vol. 345, pp. 719–724, 2008. - W.-S. Du, “A note on cone metric fixed point theory and its equivalence,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 72, no. 5, pp. 2259–2261, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - Z. Kadelburg, S. Radenović, and V. Rakočević, “Topological vector space-valued cone metric spaces and fixed point theorems,”
*Fixed Point Theory and Applications*, Article ID 170253, 18 pages, 2010. View at Zentralblatt MATH - S. Janković, Z. Kadelburg, and S. Radenović, “On cone metric spaces: a survey,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 74, no. 7, pp. 2591–2601, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. A. Krasnoseljski and P. P. Zabrejko,
*Geometrical Methods in Nonlinear Analysis*, Springer, 1984. - M. G. Kreĭn and M. A. Rutman, “Linear operators leaving invariant a cone in a Banach space,”
*Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo*, vol. 3, no. 1, pp. 3–95, 1948. View at Zentralblatt MATH - Y. J. Cho, B. E. Rhoades, R. Saadati, B. Samet, and W. Shantawi, “Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type,”
*Fixed Point Theory and Applications*, vol. 2012, article 8, 2012. - 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 · View at Zentralblatt MATH - E. Graily, S. M. Vaezpour, R. Saadati, and Y. J. Cho, “Generalization of fixed point theorems in ordered metric spaces concerning generalized distance,”
*Fixed Point Theory and Applications*, vol. 2011, article 30, 2011. - Z. M. Fadail, A. G. B. Ahmad, and Z. Golubović, “Fixed foint theorems of single-valued mapping for c-distance in cone metric spaces,”
*Abstract and Applied Analysis*, vol. 2012, Article ID 826815, 11 pages, 2012. - Z. M. Fadail and A. G. B. Ahmad, “Coupled fixed foint theorems of single-valued mapping for c-distance in cone metric spaces,”
*Journal of Applied Mathematics*, vol. 2012, Article ID 246516, 20 pages, 2012. - Z. M. Fadail and A. G. B. Ahmad, “Common coupled fixed foint theorems of single-valued mapping for c-distance in cone metric spaces,”
*Abstract and Applied Analysis*, vol. 2012, Article ID 901792, 24 pages, 2012. - Z. M. Fadail, A. G. B. Ahmad, and L. Paunović, “New fixed point results of single-valued mapping for c-distance in cone metric spaces,”
*Abstract and Applied Analysis*, vol. 2012, Article ID 639713, 12 pages, 2012. View at Publisher · View at Google Scholar - A. Singh, R. C. Dimri, and S. Bhatt, “A unique common fixed point theorem for four maps in cone metric spaces,”
*International Journal of Mathematical Analysis*, vol. 4, no. 29–32, pp. 1511–1517, 2010. View at Zentralblatt MATH - 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 - 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. - A. Amini-Harandi and M. Fakhar, “Fixed point theory in cone metric spaces obtained via the scalarization method,”
*Computers & Mathematics with Applications*, vol. 59, no. 11, pp. 3529–3534, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - Z. Kadelburg, S. Radenović, and V. Rakočević, “A note on the equivalence of some metric and cone metric fixed point results,”
*Applied Mathematics Letters*, vol. 24, no. 3, pp. 370–374, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH