Reinhardt domains and the Gleason problem
Oscar Lemmers, Jan Wiegerinck (2001)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Oscar Lemmers, Jan Wiegerinck (2001)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Samir, Lahrech, Abdessamad, Jaddar, Abdelmalek, Ouahab, Abderrahim, Mbarki (2006)
Lobachevskii Journal of Mathematics
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Kolář, Martin
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Ivanov, Vsevolod (2003)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20. In this paper we obtain some simple characterizations of the solution sets of a pseudoconvex program and a variational inequality. Similar characterizations of the solution set of a quasiconvex quadratic program are derived. Applications of these characterizations are given.
Viorel Vâjâitu (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Klas Diederich, John Erik Fornaess (1982)
Manuscripta mathematica
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Łukasz Kosiński, Tomasz Warszawski (2013)
Annales Polonici Mathematici
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In 1984 L. Lempert showed that the Lempert function and the Carathéodory distance coincide on non-planar bounded strongly linearly convex domains with real-analytic boundaries. Following his paper, we present a slightly modified and more detailed version of the proof. Moreover, the Lempert Theorem is proved for non-planar bounded strongly linearly convex domains.
Vsevolod Ivanov (2008)
Open Mathematics
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A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.
Ivanov, Vsevolod (2001)
Serdica Mathematical Journal
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First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.