Generalized contractions for a sequence of multi-valued mappings

The aim of this paper is to obtain a general result for existence of common fixed points for a sequence of multi-valued mappings on a K-quasimetric space endowed with a graph. This will enable us to present a simultaneous generalization of various types of fixed point theorems in the literature. In particular, we show that some fixed point theorems in metric spaces can be generalized to 2-quasimetric spaces.. We also provided an example to show that our results are genuine generalization of some old results.