The Convergence Of Solutions For Set-valued Differential Equations In Fr(?)chet Space

In recent years,set differential equations as the generalized form of ordinary differential equations have been widely concerned by scholars,and they have obtained the results of the existence,stability and convergence on the compact convex subset of spaces.The space of Fr(?)chet has been widely used in modern analysis,differential geometry and theoretical physics.At present,there is only a preliminary result of the set differential equations in Fr(?)chet space.This paper discusses the existence and convergence of several kinds of set differential equations in Fr(?)chet space,by taking advantage of the truth that the Fr(?)chet space can be regarded as the limit of projection of Banach space and the method of quasilinearization.By using the method of quasilinearization,we obtain quadratic convergence of set differential equations with initial conditions in Fr(?)chet space.Under the condition of caratheodory set value function,using the method of quasilinearization,we obtain the existence and the convergence for the solution of a class of neutral set value functional differential equation in Fr(?)chet space.By introducing the definition of hyperconcave and hyperconvex and using the method of quasilinearization,we prove higher order convergence for initial value problem of set differential equations with two sum of functions in Fr(?)chet space.