Abstarct: Abstract ‎In this thesis, the existence of fixed points of multi-valued contractive mappings in a special class of ‎b‎‎-metric spaces endowed with a graph ‎is investigated‎. Also some examples are provided to show that our results are true generalizations of some fixed point theorems. In addition, quasimetric spaces and cyclic weakly (ψ,φ,A,B) ‎-contractive mappings are introduced and a fixed point theorem for such mappings in complete ordered s-quasimetric spaces is proved. An example is provided that satisfies the conditions of this new theorem, while old corresponding results can not be applied for this example. Moreover, a new class of generalized contractive mappings is introduced and a common fixed point theorem for this class of mappings in complete ‎b‎-metric spaces is proved. In fact, this theorem is a generalization of some old results in this field. ‎Finally, ‎set-valued ‎generalized ‎contractive ‎mappings ‎in ‎cone ‎metric ‎spaces ‎endowed ‎with a‎ ‎graph ‎are ‎introduced ‎and a‎ ‎fixed ‎point ‎theorem ‎in ‎such ‎spaces ‎is ‎proved