Counter-examples to Breckner-convexity
DOI:
https://doi.org/10.35925/j.multi.2023.3.8Kulcsszavak:
convexity, Breckner-convexity, counter examplesAbsztrakt
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.
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2023-12-15
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