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引用次数: 0
摘要
本文研究了在弱 L 平均条件下求解巴拿赫空间中非线性方程的三步牛顿法的局部收敛性。更确切地说，当非线性算子的一阶弗雷谢特导数满足半径和中心 Lipschitz 条件且具有弱 L 平均时，我们推导出了两个存在性定理；特别是，假设 L 是正可积分函数，但不一定是非递减的，这在之前的讨论中是假设过的。
On the Existence Theorem of a Three-Step Newton-Type Method Under Weak L-Average
In the present paper, we have studied the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weak L-average. More precisely, we have derived the two existence theorems when the first-order Fréchet derivative of nonlinear operator satisfies the radius and center Lipschitz condition with a weak L-average; particularly, it is assumed that L is positive integrable function but not necessarily non-decreasing, which was assumed in the earlier discussion.
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