Abstract
This work is devoted to a systematic study of the inversion of nondecreasing one variable extended real-valued functions. Its results are preparatory for a new duality theory for quasiconvex problem [6]. However the question arises in a variety of situations and as such deserves a separate treatment. Applications to topology, probability theory, monotone rearrangements, convex analysis are either pointed out or sketched.
Zusammenfassung
In dieser Arbeit wird systematisch die Umkehrung monoton nichtfallender Funktionenf: ℝ → ℝ ∪ {−∞, +∞} studiert. Die Ergebnisse bilden die Grundlage für eine neue Dualitätstheorie quasikonvexer Probleme [6]. Da jedoch die Fragestellung bei einer ganzen Anzahl weiterer Situationen auftritt, verdient sie eine gesonderte Behandlung. Anwendungen in der Topologie, Wahrscheinlichkeitstheorie, monotonen Umordnungen und in der konvexen Analysis werden aufgezeigt und skizziert.
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Penot, J.P., Volle, M. Inversion of real-valued functions and applications. ZOR - Methods and Models of Operations Research 34, 117–141 (1990). https://doi.org/10.1007/BF01415975
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DOI: https://doi.org/10.1007/BF01415975