线性空间上凸函数的f′ejer不等式的改进与反演

IF 0.5 Q3 MATHEMATICS Problemy Analiza-Issues of Analysis Pub Date : 2020-11-01 DOI:10.15393/j3.art.2020.8830

S. Dragomir

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引用次数: 2

摘要

．设f是线性空间中凸集C和x上的一个凸函数;y 2 C;如果p = [0];1) ![0;1)是Lebesgue可积对称的，即p (1) t = p (t对于所有2 [0];1);式中r (cid:6) f()为G(cid:226)对侧导数。给出了规范和半内产品的一些应用。

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REFINEMENTS AND REVERSES OF F ́EJER’S INEQUALITIES FOR CONVEX FUNCTIONS ON LINEAR SPACES

. Let f be an convex function on the convex set C in a linear space and x; y 2 C; with x 6 = y: If p : [0 ; 1] ! [0 ; 1 ) is Lebesgue integrable and symmetric, namely p (1 t = p ( t for all 2 [0 ; 1] ; then where r (cid:6) f ( ) are the G(cid:226)teaux lateral derivatives. Some applications for norms and semi-inner products are also provided.

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