The Study Of Fixed Point Theorems In Generalized G-metric Spaces

The fixed point problem is one of the hot topics in nonlinear functional analysis,and the research on the existence and uniqueness of fixed points is particularly extensive.In this paper,we mainly study the existence and unique-ness of fixed points in generalized G-metric space under different compression mapping conditions,and obtain some new results.The main contents are as follows:1.The concept of G-cone metric space over Banach algebra is proposed.is proposed,and then the fixed point problem of different extension mappings is studied in this space.2.The definition of G*-cone metric space is given.Under the condition of irregular cones,by using cone theory and iterative techniques,the common fixed point theorem for the combination of multiple single-valued mappings and set-valued mappings is proved.3.In Gb-metric space,the concepts of FG-coupled fixed point and coin-cidence point are proposed.Combined with altering distance function ψ,the existence and uniqueness of coupling coincidence point under self-mappings and mixed mappings are proved.