论弱 L 均值条件下牛顿三步法的存在定理

IF 0.8 4区综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2024-01-27 DOI:10.1007/s40010-023-00857-5

J. P. Jaiswal

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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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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来源期刊

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 综合性期刊-综合性期刊

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

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