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.