# zbMATH — the first resource for mathematics

Common fixed points in cone metric spaces. (English) Zbl 1196.54086
From the text: We consider a notion of $$g$$-weak contractive mappings in the setting of cone metric spaces [i.e. mappings $$f\colon X\to X$$ of such a space $$X$$ which satisfy a condition of the form $d(f(x),f(y))\leq \alpha d(f(x),g(x))+\beta d(f(y),g(y))+\gamma d(g(x),g(y))$ for all $$x,y,\in X$$, where $$g: X\to X$$ and $$\alpha,\beta,\gamma\in [0,1)$$ satisfy $$\alpha+\beta+\gamma<1$$. We give results on common fixed points. These results generalize some results on common fixed points in metric spaces and some of the results of L. G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] in cone metric spaces.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces 47H10 Fixed-point theorems 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
##### Keywords:
cone metric spaces; weak contractions; common fixed points
Full Text:
##### References:
 [1] Huang L.-G., Zhang X.,Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl.,332 (2007), 1467–1475. · Zbl 1118.54022 · doi:10.1016/j.jmaa.2005.03.087
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.