一类混合单调算子方程的求解及应用

Iterative solution of some mixed monotone operators equation and applications

利用锥理论和半序方法证明了Banach空间中一类非线性二元算子方程的解的存在唯一性定理,并给出迭代序列收敛于解的误差估计,作为应用,讨论了不具有单调性的算子方程的可解性,改进并推广了已有的一些结果.

By using the cone theory and partial technique, the existence and uniqueness theorem of solutions for a class of nonlinear binary operator in Banach spaces are investigated, and the error estimates that iterative sequences converge to solutions are also given. As the applications of the resulting results, the solvability of operator equations which do not possess monotonicity are discussed. The results presented here improve and generalize some known results.