Abstract
In order to better understand the monotonicity properties which characterize the gradient of pseudoconvex and quasi convex funzions, psedomonotonicity and quasi monotonicity can be introduced.
A quite different approach is proposed in this paper, by defining new order relations, whose preservation leads precisely to several kinds of pseudoconvexity and quasi convexity.
Some general properties of order preservation are proved; they are useful to state necessary and sufficient conditions of monotonicity for particular orders related with generalized convexity.
Riassunto
Per meglio intendere le proprietà di monotonia che caratterizzano i gradienti delle funzioni pseudoconvesse e quasi convesse, si sono introdotti i concetti di pseudomonotonia e di quasi monotonia.
In questo lavoro si propone un approccio diverso definendo alcune relazioni di preordine parziale la cui preservazione conduce appunto ai vari tipi di pseudoconvessità e di quasi convessità.
Si mostrano alcune proprietà generali della preservazione di un ordinamento che si rivelano utili per formulare condizioni necessarie e condizioni sufficienti di monotonia per ordinamenti particolari legati alla convessità generalizzata.
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References
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This research is partially supported by the Italian Ministery of Education and by the National Research Council.
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Castagnoli, E., Mazzoleni, P. Order preserving functions and generalized convexity. Rivista di Matematica per le Scienze Economiche e Sociali 14, 33–46 (1991). https://doi.org/10.1007/BF02319398
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DOI: https://doi.org/10.1007/BF02319398