Banach空间中一类二元算子方程的可解性及应用

Solvability Theorems with Applications of a Binary Operator Equation in Banach Space

在新的初始条件下,利用锥理论和半序方法,研究了Banach空间中二元算子方程A(x,y)=Lx的迭代求解问题.在对算子A和L的连续性和紧性不做任何假定的情况下,证明了其解的存在性和唯一性.还证明了本文所构建的迭代序列收敛于该解,估计了其收敛速度.最后将所获结果用于讨论一类微分-积分方程解的存在性问题.

The existence of the iterative solution for the operator equation A（x, y） =- Lx is studied by the techniques of partially order and the theorem of cone in Banach space, where neither A nor L need to be continues or compactness. Besides, we con- struct some new iterative sequences and study their approximation, then we get some new theorems. Finally, we apply the new results presented in this paper to study the solvability of a class of integral-differential equation.