Bartl, David; Fabian, Marián Can Pourciau’s open mapping theorem be derived from Clarke’s inverse mapping theorem easily? (English) Zbl 1460.46003 J. Math. Anal. Appl. 497, No. 2, Article ID 124858, 14 p. (2021). Essentially, the authors study the possibility to deduce a suitable open mapping theorem (defined by B. H. Pourciau [J. Optim. Theory Appl. 22, 311–351 (1977; Zbl 0336.26008)]) from another appropriate inverse mapping theorem (set up by F. H. Clarke [Optimization and nonsmooth analysis. John Wiley, New York, NY (1983; Zbl 0582.49001)]). Reviewer: Mohammed El Aïdi (Bogotá) Cited in 3 Documents MSC: 46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness) Keywords:convex compact set of matrices; Clarke generalized Jacobian; inverse mapping theorem; open mapping theorem Citations:Zbl 0336.26008; Zbl 0582.49001 PDFBibTeX XMLCite \textit{D. Bartl} and \textit{M. Fabian}, J. Math. Anal. Appl. 497, No. 2, Article ID 124858, 14 p. (2021; Zbl 1460.46003) Full Text: DOI References: [1] Arutyunov, A. V.; Izmailov, A. F.; Zhukovskiy, A. F., Continuous selections of solutions for locally Lipschitzian equations, J. Optim. Theory Appl., 185, 3, 679-699 (2020) · Zbl 1481.47072 [2] Clarke, F. H., Optimization and Nonsmooth Analysis (1983), J. Wiley & Sons: J. Wiley & Sons New York, Singapore · Zbl 0582.49001 [3] Izmailov, A. F., On a problem of existence of a nondegeneracy subspace for a convex compact family of epimorphisms, (Bereznev, V. A., Theoretical and Applied Problems of Nonlinear Analysis (2010), Computer Center RAS: Computer Center RAS Moscow), 34-49, (in Russian) [4] Lang, S., Linear Algebra (1987), Springer-Verlag GTM: Springer-Verlag GTM New York [5] Pourciau, B. H., Analysis and optimization of Lipschitz continuous mappings, J. Optim. Theory Appl., 22, 3, 311-351 (1977) · Zbl 0336.26008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.