Banach空间中非混合单调算子的新不动点定理

The New Fixed Point Theorems for the Non-Mixed Monotone Operators in Banach Spaces

利用锥与半序理论和混合单调算子理论,研究半序Banach空间中非混合单调算子方程组A(x,x)=x B(x,x)=x解的存在与唯一性,给出了收敛于算子方程组解的逼近迭代序列和误差估计,进而获得了非混合单调算子方程A(x,x)=x和非单调算子方程Ax=x的唯一解及其解的逼近迭代序列和误差估计,并改进和推广了有关文献中的相应结果.

With the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of the solution for the systems of the non-mixed montone operator equations {A（x,x）=x B（x,x）=x are studied, and the iterative sequences which converge to the solution for system of operator equations and the error estimations are given, and the iterative solution , the iterative sequences which converge to the solution and the error estimations of the non-mixed monotone operator equations A（x,x） = x and the operator equation Ax = x are also obtained. The results of some references are improved and extended.