Fixed Point Theorems Of Convex-power Condensing Operator And Applications

In this thesis, we discussed the fixed point theorems of convex-power operator and their applications in different equations from two different aspects.Firstly, fixed point theorems of increasing and decreasing convex-power operators are obtained by noncompact measure of Kuratowski. consider the initial value problem of semilinear evolution in Banach space. The fixed point theorems are applied to the existence of mild positive solution for abstract semilinear evolution equations and especially the iterative sequences about mild solutions are given.Secondly, fixed point theorems of convex-power operators are obtained by the construction of topological degree, the properties of completely continuous operator topological degree and the calculation of fixed point index. Considering the initial value problem of nonlinear Integro-Differential equation. The new fixed point theorem is applied to nonlinear Integro-Differential equation, we get its non-zero solution.