As applications of the above zero theorem, we deduce many new mapping theorems.

By making use of contraction mapping principle and similar matrices and graphical method,this paper discusses some methods of asking its limit in accordance with recurrent sequence of number.

By contraction mapping principle,we get an optimum result in Banach space L2(a,b) of the existence and uniqueness of solutions if f satisfies L2-Carathéodory conditions.

We consider the Hilbert boundary value problem of general first order quasilinear elliptic complex equation with second order oblique derivatives (abbreviated D 2H problem),and give thier solvability results by using the contraction mapping principle.

By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness theorem of solutions for a class of nonlinear operator equations in ordered Banach spaces are investigated in more general condition.

This paper discusses a class of nonlinear equation with a parameter by means of the cone theory and Banach contraction mapping principle, it is proved that the existence and uniqueness of solutions for this kind equations and continuous dependence of solutions on the parameter.

With the cone theory and Banach contraction mapping principle,it is proved that the existence and uniqueness of solutions for a class of nonlinear operator equations without the assumption of continuity and compactness and upper-lower solutions of operators.