"secant" .
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"1463-1473" .
"Banach" .
_:N8f625e223e094c2db232e5c243d023dc _:Ndaec0be9963645ddbac7bab7d7a44d7a .
"Mathematical Sciences" .
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"Department of Mathematical Sciences, Cameron University, 73505, Lawton, OK, USA" .
_:Ne7440bf76327466d9a8edd45e294febb .
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"1579-1505" .
"Ioannis K." .
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"Stirling" .
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"Kurchatov" .
_:Ndaec0be9963645ddbac7bab7d7a44d7a .
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"Secant-type" .
"Revista de la Real Academia de Ciencias Exactas, F\u00EDsicas y Naturales. Serie A. Matem\u00E1ticas" .
_:Ndaec0be9963645ddbac7bab7d7a44d7a .
.
"paper" .
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"1578-7303" .
"The aim of this paper is to introduce general majorizing sequences for iterative procedures which may contain a non-differentiable operator in order to solve nonlinear equations involving Banach valued operators. A general semi-local convergence analysis is presented based on majorizing sequences. The convergence criteria, if specialized can be used to study the convergence of numerous procedures such as Picard\u2019s, Newton\u2019s, Newton-type, Stirling\u2019s, Secant, Secant-type, Steffensen\u2019s, Aitken\u2019s, Kurchatov\u2019s and other procedures. The convergence criteria are flexible enough, so if specialized are weaker than the criteria given by the aforementioned procedures. Moreover, the convergence analysis is at least as tight. Furthermore, these advantages are obtained using Lipschitz constants that are least as tight as the ones already used in the literature. Consequently, no additional hypotheses are needed, since the new constants are special cases of the old constants. These ideas can be used to study, the local convergence, multi-step multi-point procedures along the same lines. Some applications are also provided in this study." .
"same line" .
_:N269c1e63c090422a803630be64ee0b50 .
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_:N69c4c5e0f6194f1986130577b97afb06 .
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_:N269c1e63c090422a803630be64ee0b50 "113" .
_:N96a1fae98a9f4ff083a1be5ca16d1c0e .
"convergence" .
"Santhosh" .
"analysis" .
"Aitken" .
"Picard" .
"2018-06-30" .
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"https://scigraph.springernature.com/explorer/license/" .
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"https://doi.org/10.1007/s13398-018-0561-5" .
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"George" .
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"study" .
_:Ne7440bf76327466d9a8edd45e294febb .
"local convergence" .
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"Springer Nature" .
.
"On the complexity of choosing majorizing sequences for iterative procedures" .
"sequence" .
"old constants" .
_:Nc55df95addb147888df2bf4e26fd5865 .
"2018-06-30" .
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_:N69c4c5e0f6194f1986130577b97afb06 "2" .
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"Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, Mangalore, India" .
"convergence analysis" .
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_:N96a1fae98a9f4ff083a1be5ca16d1c0e .
_:N269c1e63c090422a803630be64ee0b50 .
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_:Nc55df95addb147888df2bf4e26fd5865 "10.1007/s13398-018-0561-5" .
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"hypothesis" .
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_:N96a1fae98a9f4ff083a1be5ca16d1c0e "Springer Nature - SN SciGraph project" .
"multi-step multi-point procedures" .
"Lipschitz constants" .
"applications" .
"2022-01-01T18:49" .
"special case" .
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"Newton-type" .
_:Nc55df95addb147888df2bf4e26fd5865 "doi" .
"Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, Mangalore, India" .
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_:N8f625e223e094c2db232e5c243d023dc .
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"complexity" .
"en" .
_:N8f625e223e094c2db232e5c243d023dc .
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"nonlinear equations" .
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_:Ne7440bf76327466d9a8edd45e294febb "pub.1105223602" .
_:Nc55df95addb147888df2bf4e26fd5865 .
"equations" .
"Pure Mathematics" .
_:N69c4c5e0f6194f1986130577b97afb06 .
"Department of Mathematical Sciences, Cameron University, 73505, Lawton, OK, USA" .
_:Ne7440bf76327466d9a8edd45e294febb "dimensions_id" .
"constants" .
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"lines" .
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