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Fixed point theorems for convex contraction mappings on cone metric spaces. (English) Zbl 1235.54021
Summary: {\it L.-G. Huang} and {\it X. Zhang} [J. Math. Anal. Appl. 332, No. 2, 1468--1476 (2007; Zbl 1118.54022)] rediscovered normal cone metric spaces and obtained the Banach contraction principle for this setting. Later on, {\it Sh. Rezapour} and {\it R. Hamlbarani} [J. Math. Anal. Appl. 345, No. 2, 719--724 (2008; Zbl 1145.54045)] showed that there are non-normal cones and that the assumption of normality is redundant.

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
65J15Equations with nonlinear operators (numerical methods)
Full Text: DOI
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