On the fixed point theory in bicomplete quasi-metric spaces

We show that some important fixed point theorems on complete metric spaces as Browder s fixed point theorem and Matkowski s fixed point theorem can be easily generalized to the framework of bicomplete quasi-metric spaces. From these generalizations we deduce quasi-metric versions of well-known fixed point theorems due to Krasnoselski and Stetsenko; Khan, Swalesh and Sessa; and Dutta and Choudhury, re- spectively. In fact, our approach shows that many fixed point theorems for φ-contractions on bicomplete quasi-metric spaces, and hence on complete G-metric spaces, are actually consequences of the corresponding fixed point theorems for complete metric spaces.