New Common Fixed Point Results for Four Maps on Cone Metric Spaces

Yan Han, Shaoyuan Xu
DOI: 10.4236/am.2011.29153                

Abstract

In this paper, some new existence and uniqueness of common fixed points for four mappings are obtained, which do not satisfy continuity and commutation on non-normal cone metric spaces. These results improve and generalize several well-known comparable results in the literature.

Keywords

Common Fixed Point; Cone Metric Space; Non-Normal Cone

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. G. Huang and X. Zhang, “Cone Metric Space and Fixed Point Theorems of Contractive Mappings,” Journal of Mathematical Analysis and Applications, Vol. 332, No. 2, 2007, pp. 1468-1476. doi:10.1016/j.jmaa.2005.03.087
[2]	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, 2008, pp. 416-420. doi:10.1016/j.jmaa.2007.09.070
[3]	M. Abbas and B. E. Rhoades, “Fixed and Periodic Point Results in Cone Metric Spaces,” Applied Mathematics Letters, Vol. 22, No. 4, 2009, pp. 511-515. doi:10.1016/j.aml.2008.07.001
[4]	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, 2010, pp. 80-86. doi:10.1016/j.amc.2010.01.003
[5]	G. X. Song, X. Y. Sun, Y. Zhao and G. T. Wang, “New Com-mon Fixed Point Theorems for Maps on Cone Metric Spaces,” Applied Mathematics Letters, Vol. 23, No. 9, 2010, pp. 1033-1037. doi:10.1016/j.aml.2010.04.032
[6]	C. D. Bari and P. Vetro, “φ-Pairs and Common Fixed Points in Cone Metric Spaces,” Rendiconti del Circolo Matematico Pa-lermo, Vol. 57, 2008, pp. 279-285.
[7]	S. Radenovic, “Common Fixed Points under Contractive Conditions in Cone Metric Spaces,” Computers and Mathematics with Applications, Vol. 58, No. 6, 2009, pp. 1273-1278. doi:10.1016/j.camwa.2009.07.035
[8]	Sh. Rezapour and R. Hamlbarani, “Some Note on the Paper ‘Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings’,”Journal of Mathematical Analysis and Applications, Vol. 345, No. 2, 2008, pp. 719-724. doi:10.1016/j.jmaa.2008.04.049