The Study Of Several Fixed Point Problems In Generalized Metric Spaces

In the discipline of nonlinear functional analysis,the fixed point problem of operators is one of the most important research topics,and the existence and uniqueness of fixed points is one of the classical problems.In this paper,the fixed point problems in cone b-metric space and D*-metric space are studied.The main results are as follows:1.By using the knowledge of generalized c-distance,the fixed point theorems of a new kind of expansive operator in cone b-metric spaces are discussed.2.By constructing iterative sequence,the theorems of common fixed points in cone b-metric space over Banach algebras are proved.3.Introducing weakly contractive mapping into the D*-metric space,and using altering distance function to prove some fixed point theorems satisfying generalized weakly contractive mapping in the complete D*-metric space.4.The definition of compatible mapping in D*-metric space is proposed,and the common fixed point theorems of multiple self-compatible mappings are discussed.