STRONG CONVERGENCE THEOREM FOR NEW FOUR-STEP ITERATIVE METHOD

被引：0

作者：

Gugnani, Meenakshi ^{[1
]}

Batra, Charu ^{[2
]}

机构：

[1] Sh LN Hindu Coll, Dept Math, Rohtak 124001, India

[2] Maharshi Dayanand Univ, Dept Math, Rohtak 124001, India

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2025年 / 15卷 / 03期

关键词：

Convergence theorem; Contractive operators; Fixed-point iterative process; FIXED-POINTS; MAPPINGS; SPACES;

D O I：

10.3934/naco.2024042

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a new iterative method, namely the J-New iterative method. We prove its strong convergence result using a contractive condition. We also study the stability of the J-New iterative method. We present a comparison theorem showing that the J-New method converges faster than the J-Hammad method. Moreover, we give numerical examples to validate the performance of our algorithm and compare the rate of convergence of the J-New algorithm with the J-Hammad, J-Khan, J-SP, J-Noor, J-Ishikawa, and J-Mann algorithms. Specifically, we show that the convergence rate of the J-New method is superior to that of the other methods mentioned, establishing it as the most efficient among the compared iterative techniques. Also, we give an application of our main result.

引用

页码：785 / 799

页数：15

共 22 条

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