Remarks on “Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings”

Recently, José R. Morales and Edixon Rojas [José R. Morales and Edixon Rojas, Cone metric spaces and fixed point theorems of TT-Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010) 175–184] proved fixed point theorems for TT-Kannan and TT-Chatterjea contractions in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this without using the normality condition. Two results for these classes of contractive mappings are also proved. Examples are given to illustrate the results.