Fixed Point Theory Of Contractive Mappings In N-Banach Spaces

The theory of fixed points actually is applied to solve the problem of the operator equation Tx = x.And it is regarded as the theoretical basis of the existence and uniqueness when dealing with many algebraic equations,integral equations and differential equations,which plays a important role in functional analysis.This paper,the existence and uniqueness of fixed points under con-tractive mapping in n-Banach spaces are proved by using iterative method to construct convergent sequences,thus extending and improving some results in literature,the main results obtained are as follows:1.Changing the contractive constant ? which is from the classical contractive mapping p(Tx,Ty)??p(x,y),? ?[0,1)into the function f(t)of one variable from[0,+?)to[0,1),it is concluded that:|| Tx-Ty,c1,…,cn-1||? f(||x-y,c1,…,cn-1||)||x-y,C1,…,Cn-1||A few different types of fixed point theorems under contractive mapping are proved.2.According to the relationship of mappings,iterative method is used to construct odd-even sequences,it is concluded that:|| Sx-Ty,c1,…,Cn-1 ||? f(||x-y,c1,…,cn-1 ||)||x-y,c1…,Cn-1 ||f(t)is the function from[0,+?)to[0,1),common fixed point theorems under contractive mappings are proved.