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Zbl 1235.54021
Alghamdi, Mohammad A.; Alnafei, Shahrazad H.; Radenović, Stojan; Shahzad, Naseer
Fixed point theorems for convex contraction mappings on cone metric spaces. (English)
[J] Math. Comput. Modelling 54, No. 9-10, 2020-2026 (2011). ISSN 0895-7177

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.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
65J15 Equations with nonlinear operators (numerical methods)

Keywords: cone metric space; convex contraction; fixed point

Citations: Zbl 1118.54022; Zbl 1145.54045

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