Replacing the real numbers as the codomain of a metric by an ordered Banach space, 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 L.-G. Huang
and 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.