关于两个非线性非单调二元算子的公共不动点定理及其应用

On Common Fixed Point Theorems of Two Nonlinear Non-monotone Two Binary Operators with Applications

在Banach空间中,利用非线性泛函分析中的锥理论和单调迭代的方法,研究了两个非线性非单调二元算子的公共不动点的存在与唯一性,并给出了逼近公共不动点的迭代序列的误差估计式;然后作为应用,得到了Banach空间中的一类非线性积分方程组的解,改进了最近的一些结果.

By using the cone theory and monotone iterative technique in nonlinear functional analysis, the existence and uniqueness of common fixed points for two nonlinear non-monotone two binary operators are discussed. The error estimate of the iterative sequences of approximation common fixed point is given. As an application, the solutions of systems of a class of nonlinear integral equations in Banach spaces are obtained. The results obtained here improve some recent results.