Some Generalizations of Fixed Point Theorems in Cone Metric Spaces

Abstract

We generalize, extend, and improve some recent fixed point results in cone metric spaces including the results of H. Guang and Z. Xian (2007); P. Vetro (2007); M. Abbas and G. Jungck (2008); Sh. Rezapour and R. Hamlbarani (2008). In all our results, the normality assumption, which is a characteristic of most of the previous results, is dispensed. Consequently, the results generalize several fixed results in metric spaces including the results of G. E. Hardy and T. D. Rogers (1973), R. Kannan (1969), G. Jungck, S. Radenovic, S. Radojevic, and V. Rakocevic (2009), and all the references therein.