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- Title
COUNTER-EXAMPLES TO BRECKNER-CONVEXITY.
- Authors
Házy, Attila; Makó, Judit
- Abstract
In this paper, we examine convexity type inequalities. Let D be a nonempty convex subset of a linear space, c>0 and α:D-D→R be a given even function. The inequality f((x+y)/2) ≤ c f(x) + c f(y) + α(x-y) (x,y ∈ 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.
- Subjects
CONVEX domains; SUBSET selection; HERMITE polynomials; HADAMARD matrices; JENSEN'S inequality
- Publication
Multidiszciplináris Tudományok, 2023, Vol 13, Issue 3, p74
- ISSN
2062-9737
- Publication type
Article
- DOI
10.35925/j.multi.2023.3.8