Existence and Uniqueness Theorems for a Three-Step Newton-Type Method under $L$-Average Conditions

Authors

  • Jai Prakash Jaiswal

DOI:

https://doi.org/10.12150/jnma.2022.650

Keywords:

Banach space, Nonlinear equation, Lipschitz condition, $L$-average, Convergence ball.

Abstract

In this paper, we study the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weaker hypothesis. More precisely, we derive the existence and uniqueness theorems, when the first-order derivative of nonlinear operator satisfies the $L$-average conditions instead of the usual Lipschitz condition, which have been discussed in the earlier study.

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Published

2024-04-10

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Issue

Vol. 4 No. 4 (2022)

Section

Articles

How to Cite

Existence and Uniqueness Theorems for a Three-Step Newton-Type Method under $L$-Average Conditions. (2024). Journal of Nonlinear Modeling and Analysis, 4(4), 650-657. https://doi.org/10.12150/jnma.2022.650