一类随机算子方程A(ω,x,x)+u_0=B(ω,x)的迭代收敛性

Random fixed point of some random operator equation A(ω,x,x)+u_0=B(ω,x)

利用锥理论和非对称迭代方法,研究了半序实Banach空间中一类随机算子方程A(ω,x(ω),x(ω))+u0=B(ω,x(ω))的随机不动点的存在唯一性,给出了迭代序列收敛于解的误差估计,把某些反向混合单调算子的不动点定理进行了随机化.

By using the cone theory and non-symmetric iteration method, this paper analyszes the exisitence and uniqueness of random fixed point of random operator equations A ( ω , x ( ω ), x ( ω )) + u0= B ( ω , x( ω)) in the semi-order real Banach space. The iteration sequences which converge to solution and the error estimates are also given, and some random versions of fixed point theorems for anti-mixed monotone operator are derived.