Study Of Several Geometric Properties Of Some Metric Spaces And Normed Spaces

The study of fixed point problem of metric spaces and the convexity and smoothness of Banach spaces have important significance and high theoretical value in the development on Banach spaces theory,which is widely applied in control theory,operator theory,approximation theory and fixed point theory.Although the research of fixed point problem is perfect,the fixed point problem in b2-metric spaces is still to be studied.The k-strict convexity and k-smoothness of n-normed spaces are very important geometric properties.The characterizations of k-strictly convex n-normed spaces and k-smooth n-normed spaces have not been fully revealed,so further research is needed.This paper mainly carries out the research work in the following two aspects1.For the study of fixed point problems,we study the existence and uniqueness of fixed point in a kind of generalized metric spaces,and establish the existence and uniqueness theorem of fixed point of self-mapping that satisfying some conditions.2.For the study of convexity and smoothness,we emphatically study the k-strict convexity and k-smoothness of n-normed spaces,and give some characterizations of these two geometric properties.Chapter 1.Research background and research status of fixed point problems in b2-metric spaces and geometry of n-normed spaces.Chapter 2.The fixed point problems in b2-metric spaces.Chapter 3.The k-strict convexity of n-normed spaces.Chapter 4.The k-smoothness of n-normed spaces.