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 generalizedconvexity properties of the underlying fu...
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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 generalizedconvexity properties of the underlying function. In this way, pure first-order characterizations of various types of generalized convex functions are obtained.
In this paper a general theorem on the replacement of the condition “for all λ in the definition of generalizedconvexity properties of lower semicontinuous functions by the condition “there exists a λ” is shown....
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Abstract: A theorem about the separation of sub- and superfunctions $\upsilon$ and $w$ by solutions of an ordinary differential equation of second order is proved, where $\upsilon \geqslant w$ throughout the g...
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Abstract: A theorem about the separation of sub- and superfunctions $\upsilon$ and $w$ by solutions of an ordinary differential equation of second order is proved, where $\upsilon \geqslant w$ throughout the given interval. Examples show that the condition imposed on the right side $f$ of the equation is sharp, and that an analogous theorem is not true for Laplace’s equation, even in the case $f \equiv 0,\upsilon$ sub- and $w$ superharmonic.
Properties of generalized convex functions, defined in terms of the generalized means introduced by Hardy, Littlewood, and Polya, are easily obtained by showing that generalized means and generalized convex functions ...
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