Quasi-contraction of Perov type

Perov (1964) [19] used the concept of vector valued metric space, and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article we study fixed point results for the new extensions of Ćirić’s quasi-contraction to cone metric space, and we give some generalized versions of the fixed point theorem of Perov. As corollaries we generalized some results of Zima (1992) [28] and Borkowski et al. (2010) [4] for a Banach space with a non normal cone. The theory is illustrated with some examples.