The aim of this paper is to prove that the envelope of hyperbolically convexfunctions is hyperbolically convex function. Furthermore, we study the standard functional operations of hyperbolically convexfunctions and...
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The aim of this paper is to prove that the envelope of hyperbolically convexfunctions is hyperbolically convex function. Furthermore, we study the standard functional operations of hyperbolically convexfunctions and introduce a class BH[a;b] of functions representable as the difference of two hyperbolically convexfunctions.
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.
In this paper, we introduce a new class of convexfunctions, which is called generalized harmonic convexfunctions on fractal sets ℝα (0 α ≤ 1). This new class of convexfunctions includes generalizedconvex functi...
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