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Common fixed point theorems for four mappings on cone metric type space. (English) Zbl 1221.54054
Replacing the real numbers as the codomain of a metric by an ordered Banach space, {\it B. Rzepecki} [Publ. Inst. Math., Nouv. Sér. 28(42), 179--186 (1980; Zbl 0482.47029)] introduced a generalization of a metric space, later called a cone metric space by {\it L.-G. Huang} and {\it X. Zhang} [J. Math. Anal. Appl. 332, No. 2, 1468--1476 (2007; Zbl 1118.54022)]. The authors of the paper under review introduce a generalization of cone metric spaces by replacing the triangle inequality with another generalized inequality. They study fixed point theorems in this generalized setting without assuming continuity of the mappings.

54H25Fixed-point and coincidence theorems in topological spaces
54E35Metric spaces, metrizability
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