一类非线性映象对的重合与极小问题

COINCIDENCE AND MINIZATION PROBLEM FOR A COUPLE OF NONLINEAR OPERATORS

本文设E为Banach空间ΩE,L,N分别为E上的零指数Fredhdm算子和集值映象,g为上的Minkowski泛函。我们研究如下二问题:Lx∈Nxinf{g(Lx-y):y∈Nx}=inf{g(z-y):Z∈,y∈Nx}的可解性条件,并得到一些不动(重合)点定理。

Let E be a Banach space,ΩE,L、N Fredholm operator with zero indexand set-valued mapping on E respectively,g the Minkowski function of Ω,we conside theconditions for solving the two problems:Lx∈Nxinf{g(Lx-y):y∈Nx}=inf{g(z-y):z∈,y∈N}and get some fixed point and coincidence theorems.