- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 573740, 8 pages
Some Equivalences between Cone -Metric Spaces and -Metric Spaces
1Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thrung Khru, Bangkok 10140, Thailand
2 Faculty of Mathematics and Information Technology Teacher Education, Dong Thap University, Cao Lanh City, Dong Thap Province 871200, Vietnam
3Journal of Science, Dong Thap University, Cao Lanh City, Dong Thap Province 871200, Vietnam
Received 20 June 2013; Revised 24 August 2013; Accepted 27 August 2013
Academic Editor: Hassen Aydi
Copyright © 2013 Poom Kumam 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.
- I. A. Bakhtin, “The contraction mapping principle in quasimetric spaces,” Functional Analysis, vol. 30, pp. 26–37, 1989.
- S. Czerwik, “Contraction mappings in -metric spaces,” Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 1, no. 1, pp. 5–11, 1993.
- M. Akkouchi, “A common fixed point theorem for expansive mappings under strict implicit conditions on b-metric spaces,” Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium. Mathematica, vol. 50, no. 1, pp. 5–15, 2011.
- M. O. Olatinwo and C. O. Imoru, “A generalization of some results on multi-valued weakly Picard mappings in -metric space,” Fasciculi Mathematici, no. 40, pp. 45–56, 2008.
- M. Păcurar, “A fixed point result for -contractions on -metric spaces without the boundedness assumption,” Fasciculi Mathematici, no. 43, pp. 127–137, 2010.
- M. Jovanović, Z. Kadelburg, and S. Radenović, “Common fixed point results in metric-type spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 978121, 15 pages, 2010.
- N. Hussain, D. Dorić, Z. Kadelburg, and S. Radenović, “Suzuki-type fixed point results in metric type spaces,” Fixed Point Theory and Applications, vol. 2012, article 126, 2012.
- N. Hussain and M. H. Shah, “KKM mappings in cone -metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 1677–1684, 2011.
- H. Huang and S. Xu, “Fixed point theorems of contractive mappings in cone b-metric spaces and applications,” Fixed Point Theory and Applications, vol. 2013, article 112, 14 pages, 2013.
- L. Shi and S. Xu, “Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 120, 2013.
- 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.
- 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.
- Y. Feng and W. Mao, “The equivalence of cone metric spaces and metric spaces,” Fixed Point Theory, vol. 11, no. 2, pp. 259–264, 2010.
- A. A. 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.
- A. Kaekhao, W. Sintunavarat, and P. Kumam, “Common fixed point theorems of c-distance on cone metric spaces,” Journal of Nonlinear Analysis and Application, vol. 2012, Article ID jnaa-00137, 11 pages, 2012.
- M. Khani and M. Pourmahdian, “On the metrizability of cone metric spaces,” Topology and Its Applications, vol. 158, no. 2, pp. 190–193, 2011.
- W. S. Du and E. Karapinar, “A note on cone b-metric and its related results: generalizations or equivalence?” Fixed Point Theory and Applications, vol. 2013, article 210, 6 pages, 2013.