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Seven kinds of monotone maps

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Known as well as new types of monotone and generalized monotone maps are considered. For gradient maps, these generalized monotonicity properties can be related to generalized convexity properties of the underlying function. In this way, pure first-order characterizations of various types of generalized convex functions are obtained.

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Karamardian, S., Schaible, S. Seven kinds of monotone maps. J Optim Theory Appl 66, 37–46 (1990).

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