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dc.contributor.authorShobha, M.E.
dc.contributor.authorGeorge, S.
dc.contributor.authorKunhanandan, M.
dc.date.accessioned2020-03-31T06:51:25Z-
dc.date.available2020-03-31T06:51:25Z-
dc.date.issued2014
dc.identifier.citationJournal of Integral Equations and Applications, 2014, Vol.26, 1, pp.91-116en_US
dc.identifier.uri10.1216/JIE-2014-26-1-91
dc.identifier.urihttp://idr.nitk.ac.in/jspui/handle/123456789/9764-
dc.description.abstractIn this paper regularized solutions of ill-posed Hammerstein type operator equation KF(x) = y, where K : X ? Y is a bounded linear operator with non-closed range and F : X ? X is non-linear, are obtained by a two step Newton type iterative method in Hilbert scales, where the available data is y? in place of actual data y withen_US
dc.description.abstracty-y?en_US
dc.description.abstract? ?. We require only a weaker assumptionen_US
dc.description.abstractF'(x0)xen_US
dc.description.abstract?en_US
dc.description.abstractxen_US
dc.description.abstract-b compared to the usual assumptionen_US
dc.description.abstractF'(x?)xen_US
dc.description.abstract?en_US
dc.description.abstractxen_US
dc.description.abstract-b, where x? is the actual solution of the problem, which is assumed to exist, and x0 is the initial approximation. Two cases, viz-aviz, (i) when F'(x0) is boundedly invertible and (ii) F'(x0) is non-invertible but F is monotone operator, are considered. We derive error bounds under certain general source conditions by choosing the regularization parameter by an a priori manner as well as by using a modified form of the adaptive scheme proposed by Perverzev and Schock . 2014 Rocky Mountain Mathematics Consortium.en_US
dc.titleA two step newton type iteration for ill-posed Hammerstein type operator equations in Hilbert scalesen_US
dc.typeArticleen_US
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