Banach空间中非单调二元算子方程组的迭代求解

利用锥与半序理论和混合单调算子理论,研究半序Banach空间中非单调二元算子方程组A(x,x)=xB(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,进而获得了非单调二元算子方程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.

Iterative Solution for the Binary Non-Monotone Operator Equations in Banach Spaces

With the cone and partial ordering theory and mixed monotone operator theory,the existence and u-niqueness of the solution for the systems of binary non-montone operator equationsA(x,x)=x B(x,x)=xare studied,and the iterative sequences which converge to the solution for system of operator equations and the error estima-tions are given,and the iterative solution,the iterative sequences which converge to the solution and the error es-timations of binary non-monotone operator equationsA(x,x)=xand operator equationsAx=xare also ob-tained.The results of some references are improved and extended.