Nearness of nonlinear operators
type: Item
instance of: scholarly article
title: Nearness of nonlinear operators
author: Dimosthenis Drivaliaris
author: Yiannis Karagiorgos
author: Nikos Yannakakis
publication date: 2021-08-20T00:00:00Z
review text: The authors of this well-written and illuminating paper first introduce the notion of adequate nearness (a-nearness, for short) between Banach space valued operators and then show that if an operator \(A\) is a-near an operator \(B\), then \(A\) acquires nice properties from \(B\). For instance, if \(B\) is bijective and \(A\) is a-near \(B\), then \(A\) is bijective too. So, even though the notion of a-nearness is significantly weaker than that of nearness, a concept introduced by \textit{S. Campanato} [Rend. Accad. Naz. Sci. Detta XL, V. Ser. 13, No. 1, 307--321 (1989, Zbl 0702.35084)], it is still sufficient to yield existence and uniqueness results for operator equations. An application to the study of certain second order partial differential operators with no variational structure is also presented.
reviewed by: Simeon Reich
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 46C50
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 7383972
zbMATH Keywords: nearness
zbMATH Keywords: non-variational problem
zbMATH Keywords: discontinuous coefficients
MaRDI profile type: Publication
full work available at URL: s12215-020-00542-1
OpenAlex ID: W3088325690
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DOI: 10.1007/S12215-020-00542-1
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 7383972