Couple Fixed Point on Cone Metric Spaces

Abstract

In this article, some cople fixed point theorems are proved for the class of cone-Banach valued metric spaces over normal cones without regularity.

Key Words: Cone Metric Spaces, Fixed Point Theory

Keywords

• Cone Metric Spaces, Fixed Point Theory

References

1. Abdeljawad T., Karapınar, E. “Quasi-Cone Metric Spaces and Generalizations of Caristi Kirk's Theorem” Fixed Point Theory Appl., vol. 2009, Article ID 574387, 9 pages, 2009. doi:10.1155/2009/574387
2. Abdeljawad T., Karapınar, E. “A Common Fixed Point Theorem of a Gregus Type on Convex Cone Metric Spaces” J. Comput. Anal. Appl (to appear)
3. Abdeljawad, T.: “Completion of cone metric spaces”, Hacet. J. Math. Stat., 39(1):67-74 (2010).
4. Abdeljawad, T., Turkoglu, D., Abuloha, M.: “Some theorems and examples of cone metric spaces”, J. Comput. Anal. Appl., 12(4):739-753(2010).
5. Altun, I., Durmaz, G.: “Some fixed point theorems on ordered cone metric spaces”, Rend. Circ. Mat. Palermo 58(2):319-325 (2009).
6. Bhaskar, T.G., Lakshmikantham, V. “Fixed Point Theory in partially ordered metric spaces and applications”, Nonlinear Anal., 65:1379-1393(2006).
7. Long-Guang, H., Xian, Z., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 332:1468-1476 (2007).
8. Karapınar, E., “Fixed Point Theorems in Cone Banach Spaces”, Fixed Point Theory Appl., Article ID 609281, 9 pages, doi:10.1155/2009/609281. (2009)

9. Karapınar, E.: “Some Fixed Point Theorems on the Cone Banach Spaces”, Proc. of 7 ISAAC Congress, World Scientic, 606-612 (2010).
10. Khan, M.S. and Imdad, M.A.: “A common fixed point theorem for a class of mappings”, Indian J. Pure Appl. Math.14:1220-1227 (1983).
11. Lin, Shy-Der: “A common fixed point theroem in abstract spaces”, Indian J. Pure Appl. Math., 18(8):685-690 (1987).
12. Nieto, J. J., Rodriguez-Lopez, R., “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations”, Order, 2005 (22): 3,223--239 (2006).
13. Rezapour, Sh., Hamlbarani, R., “Some notes on the paper :Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 347,719--724 (2008).
14. Rezapour, Sh., “A review on topological properties of cone metric spaces”, Analysis, Topology and Applications Vrinjacka Banja, Serbia, Serbia, from May 30 to June 4, 2008.
15. Rzepecki, B.: “On fixed point theorems of Maia type, Publications”, De L'institut Mathématique, 28:179-186 (1980) .
16. Turkoglu, D., Abuloha, M., “Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings”, Acta Mathematica Sinica, English Series, 26(3):489-496 (2010).
17. Turkoglu, D., Abuloha, M., Abdeljawad, T. “KKM mappings in cone metric spaces and some fixed point theorems”, Nonlinear Anal.,72(1):348-353 (2010). doi:10.1016.na.2009.6.58.