Couple Fixed Point on Cone Metric Spaces

Year 2011, Volume: 24 Issue: 1, 51 - 58, 14.01.2011

Erdal Karapınar

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

• 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
• Abdeljawad T., Karapınar, E. “A Common Fixed Point Theorem of a Gregus Type on Convex Cone Metric Spaces” J. Comput. Anal. Appl (to appear)
• Abdeljawad, T.: “Completion of cone metric spaces”, Hacet. J. Math. Stat., 39(1):67-74 (2010).
• Abdeljawad, T., Turkoglu, D., Abuloha, M.: “Some theorems and examples of cone metric spaces”, J. Comput. Anal. Appl., 12(4):739-753(2010).
• Altun, I., Durmaz, G.: “Some fixed point theorems on ordered cone metric spaces”, Rend. Circ. Mat. Palermo 58(2):319-325 (2009).
• Bhaskar, T.G., Lakshmikantham, V. “Fixed Point Theory in partially ordered metric spaces and applications”, Nonlinear Anal., 65:1379-1393(2006).
• Long-Guang, H., Xian, Z., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 332:1468-1476 (2007).
• Karapınar, E., “Fixed Point Theorems in Cone Banach Spaces”, Fixed Point Theory Appl., Article ID 609281, 9 pages, doi:10.1155/2009/609281. (2009)
• Karapınar, E.: “Some Fixed Point Theorems on the Cone Banach Spaces”, Proc. of 7 ISAAC Congress, World Scientic, 606-612 (2010).
• 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).
• Lin, Shy-Der: “A common fixed point theroem in abstract spaces”, Indian J. Pure Appl. Math., 18(8):685-690 (1987).
• 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).
• 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).
• 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.
• Rzepecki, B.: “On fixed point theorems of Maia type, Publications”, De L'institut Mathématique, 28:179-186 (1980) .
• 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).
• 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.