Year: 2022
Author: Jai Prakash Jaiswal
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2022.650
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 4 : pp. 650–657
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Banach space Nonlinear equation Lipschitz condition $L$-average Convergence ball.