Approximation of solutions of nonlinear integral equations of Hammerstein type with Lipschitz and bounded nonlinear operators
type: Item
instance of: scholarly article
title: Approximation of solutions of nonlinear integral equations of Hammerstein type with Lipschitz and bounded nonlinear operators
zbMATH Open document ID: 1264.65212
DOI: 10.5402/2012/963802
published in: ISRN Applied Mathematics
publication date: 2013-06-11T00:00:00Z
review text: Summary: Let \(E\) be a reflexive real Banach space with uniformly Gâteaux differentiable norm and \(F\), \(K : E \to E\) be Lipschitz accretive maps with \(D(K) = R(F) = E\). Suppose that the Hammerstein equation \(u + KFU = 0\) has a solution. An explicit iteration method is shown to converge strongly to a solution of the equation. No invertibility assumption is imposed on \(K\) and the operator \(F\) is not restricted to be angle-bounded. Our theorems are significant improvements on important recent results.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 6172994
author: N. Djitté
author: Moustapha Sene
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/963802
OpenAlex ID: W2063631363
Wikidata QID: Q58905563
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description: scientific article; zbMATH DE number 6172994