COUNTER-EXAMPLES CONCERNING BRECKNER-CONVEXITY

被引：0
|
作者：
Hazy, Attila [1 ]
Mako, Judit [1 ]
机构：
[1] Univ Miskolc, Inst Math, H-3515 Miskolc, Hungary
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2024年 / 27卷 / 01期
关键词：
Approximate convexity; Breckner-convexity; lower and upper Hermite-Hadamard inequalities; STABILITY;
D O I：
10.7153/mia-2024-27-09
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we examine convexity type inequalities. Let D be a nonempty convex subset of a linear space, c > 0 and alpha : D-D -> R be a given even function. The inequality f (x+y/2) <= cf(x) +cf(y) + alpha(x-y) (x,y is an element of D) is the focus of our examinations. We will construct an example to show that for c = 1, this Jensen type inequality does not imply the convexity of the function. Then, we compare this inequality with Hermite-Hadamard type inequalities.
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页码：127 / 135
页数：9
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