Remarks on “Quasi-contraction on a cone metric space”

Recently, D. Ilić and V. Rakočević [D. Ilić, V. Rakočević, Quasi-contraction on a cone metric space, Appl. Math. Lett. (2008) doi:10.1016/j.aml.2008.08.011] proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this and some related results without using the normality condition.