A common fized point theorem for densifying mappings;

Under the ordered conditions and noncompactness measure conditions,the existence of positive periodic solution for second-order ordinary differential equation in Banach space was proved by accurately calculating the measure of noncompactness and employing fixed-point index theorems of condensing map.

Under the nonmonotone conditions,the results of existence of periodic boundary value problem of second order ordinary differential equation in Banach space is obtained by employing measure of noncompactness,degree of condensing map and Sadvoskii fixed point theorem.

The theory of non-compactness measure and Sadovskii fixed point theorem of condensing map are applied to these problems,and some existence results are obtained.

Fixed point theorems for condensing mappings and the solvability of equation Ax+Bx+Cx=x;

Some results for condensing mapping perturbations with toplogy degree theory are established with some extended results of compact perturbations.

Altman s Theorem is further improved and some new fixes-point theorems for condensing mapping or P 1-compact mappings are set up by topology theory.

We study the solvability of 0∈(R(T+C)) making use of condensing mappings′degree theorey.

Under an order condition of nonlinear term which could be easily verified, the existence of positive solutions is proved by the topological degree theory of condensing mapping.

Under more general conditions,an existence result of positive solutions was obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.

The corresponding results on condensive mapping are discussed in section 3.

The definition of Ψ*Ψ*-condensing map on generalized convex spaces was introduced,and its some properties and fixed point theorems were given,finally existence problems of maximal element and existence problem of equilibrium point in abstract economy system were discussed as their applications.