The Fixed Point Theorem On The Compression Of C-type Functions In Rectangular B-metric Space

In this paper,we discuss the fixed point theorems for some contractions on the C-class functions in the complete rectangular b-metric space.Firstly,we give the concept of generalized ?-?-?-?-F contraction by combining the C-class functions.And we provethatthis contractive mapping has a unique fixed pointunder certain conditions by using the iterative method and with the aid of triangular ?-admissible in the rectangular metric space.The fixed point conclusions for the C-class function in the generalized metric space are extended to the rectangular metric space.One example is given to support the result.We also prove an application to a nonlinear integral equation.The second part of paper,we introduce the concept of ?-F(?,?)contraction,improve the fixed point results of weakly contractive mapping,and continues to discuss the fixed point theorem of ?-F(?,?)contractive mapping in the rectangular b-metric space of the C-class function under the triangular ?-admissible mapping.The third part of paper,we prove the common fixed point theorem for four mappings by using weak*compatibility of the mapping in the complete rectangular metric space,and give some corollary.