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

Year 2025, Volume: 74 Issue: 3, 446 - 459, 23.09.2025

Chandni Kumari , P. K. Parida , Babita Mehta

https://doi.org/10.31801/cfsuasmas.1426562

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 $\mathbb{B}$-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.

Keywords

Modified Newton-like method , Banach Space , majorant condition , local convergence , Kantorovich-type condition , Smale-type condition

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