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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
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[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
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