On the Existence Theorem of a Three-Step Newton-Type Method Under Weak L-Average

In the present paper, we have studied the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weak L -average. More precisely, we have derived the two existence theorems when the first-order Fréchet derivative of nonlinear operator satisfies th...

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Bibliographic Details
Published in:National Academy of Sciences, India. Proceedings. Section A. Physical Sciences India. Proceedings. Section A. Physical Sciences, 2024-04, Vol.94 (2), p.227-233
Main Author: Jaiswal, J. P.
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Banach spaces
Existence theorems
Lipschitz condition
Molecular
Nonlinear equations
Operators (mathematics)
Optical and Plasma Physics
Physics
Physics and Astronomy
Quantum Physics
Scientific Research Paper
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Summary:In the present paper, we have studied the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weak L -average. More precisely, we have derived the two existence theorems when the first-order Fréchet derivative of nonlinear operator satisfies the radius and center Lipschitz condition with a weak L -average; particularly, it is assumed that L is positive integrable function but not necessarily non-decreasing, which was assumed in the earlier discussion.
ISSN:0369-8203
2250-1762
DOI:10.1007/s40010-023-00857-5