The Fixed Point Theorems Of Several Types Of Contraction Mappings On Rectangular B-metric Spaces

In this paper,we firstly gave the definition of(?,?)rational type contractive mappings in the setting of rectangular b-metric space.Then we proved the existence and uniqueness of the fixed point for such kind of generalized nonlinear contractive mappings under special conditions by using the iterative method and with the aid of triangular ?-admissible mapping.We generalized the fixed point theorem of (?,?)rational type contractive mapping in the setting of rectangular metric space,and obtained a new fixed point theorem of rectangular b-metric space.The second part of paper,we introduced the concept of sequentially convergent.Then by means of a new mapping which satisfied the sequence convergence,we researched the existence and uniqueness of fixed points of an iterative sequence in the rectangular b-metric space.The third part of paper,we developed the fixed point theorem of Khan contractive mapping,and obtained a fixed point result of Khan contractive mapping in the rectangularb-metric space.