Some new coincidence and common fixed point theorems in cone metric spaces

Abstract

In this paper, the fixed point theorems without the assumption of normality are investigated, and our results generalize the main result in Abbas and Rhoades (Appl. Math. Lett. 22:511–515, 2009). Subsequently, some new fixed point theorems are obtained, and the main result in Song et al. (Appl. Math. Lett. 23:1033–1037, 2010), Abbas and Jungck (J. Math. Anal. Appl. 341:416–420, 2008) are generalized. Most important, all of our results are obtained without the assumption of normality. Finally an example is given to verify one of our results.