Local convergence analysis of modified Newton-like method under majorant condition

Chandni Kumari; P. K. Parida

Article Details

Local convergence analysis of modified Newton-like method under majorant condition

Authors:

Chandni Kumari | P. K. Parida

Publisher:

Ankara University

Main Topics:

Numerical Analysis

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.446-459

Document Type:

Article

Publication Date:

9/2025

Document Language:

English

Document ID (Org No.):

2001357869

pISSN:

1303-5991

Keywords:

Abstract:

 This article has devoted to study of local convergence analysis of a modified Newton-like method of order three to approximate a locally unique zero of a non-linear operator in mathbbB-space Banach space. Here, we mainly proved the convergence of the method by using a new type of majorant condition instead of usual majorizing sequences and recurrence relations and provide a computable error bounds. Furthermore, we will establish the relationship between majorant function with special cases like Smale-type and Kantorovich-type functions. A few favorable numerical examples has also provided to show applicability of our analysis.

 This article has devoted to study of local convergence analysis of a modified Newton-like method of order three to approximate a locally unique zero of a non-linear operator in mathbbB-space Banach space. Here, we mainly proved the convergence of the method by using a new type of majorant condition instead of usual majorizing sequences and recurrence relations and provide a computable error bounds. Furthermore, we will establish the relationship between majorant function with special cases like Smale-type and Kantorovich-type functions. A few favorable numerical examples has also provided to show applicability of our analysis.

 This article has devoted to study of local convergence analysis of a modified Newton-like method of order three to approximate a locally unique zero of a non-linear operator in mathbbB-space Banach space. Here, we mainly proved the convergence of the method by using a new type of majorant condition instead of usual majorizing sequences and recurrence relations and provide a computable error bounds. Furthermore, we will establish the relationship between majorant function with special cases like Smale-type and Kantorovich-type functions. A few favorable numerical examples has also provided to show applicability of our analysis.

 This article has devoted to study of local convergence analysis of a modified Newton-like method of order three to approximate a locally unique zero of a non-linear operator in mathbbB-space Banach space. Here, we mainly proved the convergence of the method by using a new type of majorant condition instead of usual majorizing sequences and recurrence relations and provide a computable error bounds. Furthermore, we will establish the relationship between majorant function with special cases like Smale-type and Kantorovich-type functions. A few favorable numerical examples has also provided to show applicability of our analysis.

Article Details

Local convergence analysis of modified Newton-like method under majorant condition

Authors:

Chandni Kumari | P. K. Parida

Publisher:

Ankara University

Main Topics:

Numerical Analysis

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.446-459

Document Type:

Article

Publication Date:

9/2025

Document Language:

English

Document ID (Org No.):

2001357869

pISSN:

1303-5991

Modified Newton-like method

Banach Space

majorant condition

local convergence

Kantorovich-type condition

Smale-type condition

Issues

Article Details

Local convergence analysis of modified Newton-like method under majorant condition

Authors: Chandni Kumari | P. K. Parida

Publisher: Ankara University

Main Topics: Numerical Analysis

Journal: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.446-459

Document Type: Article

Publication Date: 9/2025

Document Language: English

Document ID (Org No.): 2001357869

pISSN: 1303-5991

Modified Newton-like method

Banach Space

majorant condition

local convergence

Kantorovich-type condition

Smale-type condition

Issues

Authors:

Chandni Kumari | P. K. Parida

Publisher:

Ankara University

Main Topics:

Numerical Analysis

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.446-459

Document Type:

Article

Publication Date:

9/2025

Document Language:

English

Document ID (Org No.):

2001357869

pISSN:

1303-5991