Abstract
In this paper we introduce a weak contractive condition, called weakly φ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which ensures existence and uniqueness of common fixed points for such mappings. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abbas, M., Jungck, G.: Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416–420
Arshad, M., Azam, A., Vetro, P.: Some common fixed point results in cone metric spaces, Fixed point theory Appl., 2009 (2009), Article ID 493965
Azam, A., Arshad, M., Beg, I.: Common fixed points of two maps in cone metric spaces, Rend. Circ. Mat. Palermo, 57 (2008), 433–441
Di Bari, C., Vetro, P.: φ-pairs and common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 57 (2008), 279–285
He, Y.-M., Wang, H.-J.: Fractal image decoding based on extended fixed-point theorem. In Proceedings of the International Conference on Machine Learning and Cybernetics. Dalian, China, August (2006), 4160–4163
Huang, L.-G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1467–1475
Ilic, D., Rakocevic, V.: Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341 (2008), 876–882
Jungck, G., Radenovic, S., Radojevic, S., Rakocevic, V.: Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed point theory Appl., 2009 (2009), Article ID 643840
Leibovic, K.: The principle of contraction mapping in nonlinear and adaptive control systems, IEEE Trans. Automatic Control, 9 (1964) 393–398
Raja, P., Vaezpour, S.M.: Some Extensions of Banach’s Contraction Principle in Complete Cone Metric Spaces, Fixed Point Theory Appl., 2008 (2008), Article ID 768294, 11 pp., doi:10.1155/2008/768294
Rakowski, W.: The fixed point theorem in computing magnetostatic fields in a nonlinear medium, IEEE Trans. Magnetics, 18 (1982) 391–392
Rezapour, Sh., Hamlbarani, R.: Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345 (2008), 719–724
Steck, J.E.: Convergence of recurrent networks as contraction mappings. In Proceedings of the International Joint Conference on Neural Networks. Baltimore, Md, USA, 3 (1992),462–467
Vetro, P.: Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 56 (2007), 464–468
Author information
Authors and Affiliations
Corresponding author
Additional information
The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.
Rights and permissions
About this article
Cite this article
Di Bari, C., Vetro, P. Weakly φ-pairs and common fixed points in cone metric spaces. Rend. Circ. Mat. Palermo 58, 125–132 (2009). https://doi.org/10.1007/s12215-009-0012-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12215-009-0012-4