On the convergence of Homeier method and its extensions

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dc.contributor.authorMuhammed Saeed, K.
dc.contributor.authorKrishnendu, R.
dc.contributor.authorGeorge, S.
dc.contributor.authorPadikkal, J.
dc.date.accessioned2026-02-05T09:26:24Z
dc.date.issued2022
dc.description.abstractA third-order Homeier method for solving equations in Banach space is studied. Using assumptions on the first and second derivatives, we obtained third-order convergence. Our technique does not involve Taylor series expansion and can be extended to similar higher-order methods. We have given two extensions of the method with orders five and six. Examples with radii of convergence and basins of attraction are provided. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.
dc.identifier.citationJournal of Analysis, 2022, , , pp. -
dc.identifier.issn9713611
dc.identifier.urihttps://doi.org/10.1007/s41478-022-00449-3
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/22924
dc.publisherSpringer Science and Business Media B.V.
dc.subjectBanach space
dc.subjectConvergence order
dc.subjectHomeier method
dc.subjectIterative methods
dc.subjectTaylor expansion
dc.titleOn the convergence of Homeier method and its extensions

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