PDF(458 KB)
PDF(458 KB)
PDF(458 KB)
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 construct 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.
锥理论 / 半序方法 / 二元算子方程 / 迭代解 {{custom_keyword}} /
cone theorem / partially order / binary operator equation / iterative solution {{custom_keyword}} /
[1] Guo D. J., Lakshmikantham V., Coupled fixed points of nonlinear operators with applications, Nonlinear Anal., 1987, 11(5):623-632.
[2] Sun J. X., Liu L. S., An iterative solution method for nonlinear operator equations and its applications (in Chinese), Acta Mathematica Scientia A, 1993, 13(2):141-145.
[3] Zhang Z. T., New fixed point theorems of mixed monotone operators and applications, J. Math. Anal. Appl., 1996, 204(1):307-319.
[4] Zhang Z. T., Fixed point theorems of mixed monotone operators and its applications, Acta Math. Sin., Chin. Ser., 1998, 41(6):1121-1126.
[5] Wu Y. S., Li G. Z., On the fixed point existence and uniqueness theorems of mixed monotone operators and their applications, Acta Math. Sin., Chin. Ser., 2003, 46(1):161-166.
[6] Zhang X., Fixed point theorems of monotone mappings and coupled fixed point theorems of mixed monotone mappings in ordered metric space, Acta Math. Sin., Chin. Ser., 2001, 44(4):641-646.
[7] Liu Z., Zhu C. X., Solvability theorems with applications of an operator equation in partial order space, Acta Math. Sin., Chin. Ser., 2009, 52(6):1181-1188.
[8] Feng Y. Q., Liu S. Y., Solvability of an operator equation in partial order space, Acta Math. Sin., Chin. Ser., 2003, 46(2):411-416.
国家自然科学基金资助项目（11361042）；中央高校基本科研业务费专项资金项目（JBK1307050）
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