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Fixed and periodic point results in cone metric spaces. (English) Zbl 1167.54014
Summary: L.-G. Haung and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] proved some fixed point theorems in cone metric spaces. In this work we prove some fixed point theorems in cone metric spaces, including results which generalize those from Huang and Zhang’s work. Given the fact that, in a cone, one has only a partial ordering, it is doubtful that their Theorem 2.1 can be further generalized. We also show that these maps have no nontrivial periodic points.

54H25 Fixed-point and coincidence theorems (topological aspects)
Full Text: DOI
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