BALL CONVERGENCE FOR A CLASS OF ROOT-FINDING METHODS IN BANACH SPACE UNDER WEAK CONDITIONS

被引：0

作者：

Argyros, Ioannis K. ^{[1
]}

George, Santhosh ^{[2
]}

机构：

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[2] NIT Karnataka, Dept Math & Computat Sci, Mangalore 575025, India

来源：

ADVANCES AND APPLICATIONS IN MATHEMATICAL SCIENCES | 2020年 / 19卷 / 03期

关键词：

Chebyshev-Halley-type methods; Newton's method; Banach space; Ball convergence; Frechet-derivative; convergence order; SEMILOCAL CONVERGENCE; FAMILY; ORDER;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present the ball convergence for a class of root-finding methods in a Banach space setting of convergence order at least six. In contrast to earlier studies using hypotheses up to the second Frechet-derivative although such derivatives do not appear in the method, we only use the first derivative. Thus, we extend the applicability of these methods. In the examples, we solve systems of nonlinear equations as well as integral equations, especially in cases that cannot be covered with results from earlier studies.

引用

页码：145 / 157

页数：13

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