Counter-examples to Breckner-convexity

Authors

  • Attila Házy University of Miskolc
  • Judit Tóthné Makó University of Miskolc

DOI:

https://doi.org/10.35925/j.multi.2023.3.8

Keywords:

convexity, Breckner-convexity, counter examples

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.

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Published

2023-12-15