Nearness of nonlinear operators
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.
scientific article; zbMATH DE number 7383972
scientific article