Abstract
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.
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Acknowledgements
The author thanks the Department of Science and Technology, New Delhi, India, for approving the proposal under the scheme FIST Program (Ref. No. SR/FST/MS/2022/122 dated 19/12/2022).
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Jaiswal, J.P. On the Existence Theorem of a Three-Step Newton-Type Method Under Weak L-Average. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 94, 227–233 (2024). https://doi.org/10.1007/s40010-023-00857-5
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DOI: https://doi.org/10.1007/s40010-023-00857-5