Common fixed points for maps on cone metric space. (English) Zbl 1156.54023

Ilić, Dejan; Rakočević, Vladimir

J. Math. Anal. Appl. 341, No. 2, 876-882 (2008).

L.-G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] have replaced the real numbers by an ordered Banach space to define cone metric spaces. In this paper, the authors generalize certain common fixed point theorems of L. B. Ćirić [Proc. Am. Math. Soc. 45, 267–273 (1974; Zbl 0291.54056)], K. M. Das and K. Viswanatha Naik [ibid. 77, 369–373 (1979; Zbl 0418.54025)], L.-G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)], and G. Jungck [Am. Math. Mon. 83, 261–263 (1976; Zbl 0321.54025)] to cone metric spaces.

Reviewer: Nawab Hussain (Jeddah)

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54F05	Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

Keywords:

common fixed point; cone metric

Citations:

Zbl 1118.54022; Zbl 0291.54056; Zbl 0418.54025; Zbl 0321.54025

References:

[1]	Ćirić, Lj.B., A generalization of Banach’s contraction principle, Proc. amer. math. soc., 45, 267-273, (1974) · Zbl 0291.54056
[2]	Das, K.M.; Naik, K.V., Common fixed point theorems for commuting maps on a metric space, Proc. amer. math. soc., 77, 3, 369-373, (1979) · Zbl 0418.54025
[3]	Gajić, Lj.; Rakočević, V., Pair of non-self-mappings and common fixed points, Appl. math. comput., 187, 999-1006, (2007) · Zbl 1118.54304
[4]	Huang, L.-G.; Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings, J. math. anal. appl., 332, 1468-1476, (2007) · Zbl 1118.54022
[5]	Jungck, G., Commuting maps and fixed points, Amer. math. monthly, 83, 261-263, (1976) · Zbl 0321.54025
[6]	Rakočević, V., Functional analysis, (1994), Naučna knjiga Beograd