A note on generalized operator quasicontractions in Cone Metric Spaces

Abstract

In a recent paper [Fixed point theorem for generalized operator quasi-contractive mappings in cone metric spaces, Afrika Mat., DOI 10.1007/ s13370-012-0105-7], X. Zhang has used bounded positive definite linear operators on the given Banach space in an attempt to obtain a more general fixed point result in a normal cone metric space. We will show in this paper that most of the conditions in his theorem are superfluous and that the proof can be obtained in amuch easier way, by reducing it to a well known Ćirić's result on quasicontractions in standard metric spaces.