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Volume 4, Issue 4
Existence and Uniqueness Theorems for a Three-Step Newton-Type Method under $L$-Average Conditions

Jai Prakash Jaiswal

DOI: 10.12150/jnma.2022.650

J. Nonl. Mod. Anal., 4 (2022), pp. 650-657.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-650, author = {Prakash Jaiswal , Jai}, title = {Existence and Uniqueness Theorems for a Three-Step Newton-Type Method under $L$-Average Conditions}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {4}, number = {4}, pages = {650--657}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.650}, url = {http://global-sci.org/intro/article_detail/jnma/21903.html} }
TY - JOUR T1 - Existence and Uniqueness Theorems for a Three-Step Newton-Type Method under $L$-Average Conditions AU - Prakash Jaiswal , Jai JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 650 EP - 657 PY - 2023 DA - 2023/08 SN - 4 DO - http://doi.org/10.12150/jnma.2022.650 UR - https://global-sci.org/intro/article_detail/jnma/21903.html KW - Banach space, Nonlinear equation, Lipschitz condition, $L$-average, Convergence ball. AB -

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.

Jai Prakash Jaiswal. (2023). Existence and Uniqueness Theorems for a Three-Step Newton-Type Method under $L$-Average Conditions. Journal of Nonlinear Modeling and Analysis. 4 (4). 650-657. doi:10.12150/jnma.2022.650
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