Unified Convergence Analysis of Certain At Least Fifth Order Methods

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dc.contributor.authorSadananda, R.
dc.contributor.authorGopal, M.
dc.contributor.authorGeorge, S.
dc.contributor.authorArgyros, I.K.
dc.date.accessioned2026-02-03T13:20:26Z
dc.date.issued2025
dc.description.abstractA class of iterative methods was developed by Xiao and Yin in 2015 and obtained convergence order five using Taylor expansion. They had imposed the conditions on the derivatives of the involved operator of order at least up to four. In this paper, the order of convergence is achieved by imposing conditions only on the first two derivatives of the operator involved. The assumptions under consideration are weaker and the analysis is done in the more general setting of Banach spaces without using Taylor series expansion. The semi-local convergence analysis is also given. Further, the theory is justified by numerical examples. © 2024, SINUS Association. All rights reserved.
dc.identifier.citationCarpathian Journal of Mathematics, 2025, 41, 2, pp. 479-502
dc.identifier.issn15842851
dc.identifier.urihttps://doi.org/10.37193/CJM.2025.02.14
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/20494
dc.publisherSINUS Association
dc.subjectBanach space
dc.subjectFrèchet derivative
dc.subjectIterative methods
dc.subjectLocal convergence
dc.subjectOrder of convergence
dc.subjectSemi-local convergence
dc.titleUnified Convergence Analysis of Certain At Least Fifth Order Methods

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