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Fixed point theorems for convex contraction mappings on cone metric spaces. (English) Zbl 1235.54021
Summary: L.-G. Huang and 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, Sh. Rezapour and 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.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
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