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  • 1 Institute of Mathematics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary
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Abstract

Let X be a real linear space and be a nonempty convex subset. Given an error function E:[0,1]×(DD)→ℝ∪{+∞} and an element , a function f:D→ℝ is called (E,t)-convex if
ea
for all x,yD. The main result of this paper states that, for all a,b∊(ℕ∪{0})+{0,t,1−t} such that {a,b,a+b}∩ℕ≠, every (E,t)-convex function is also -convex, where
eb
As a consequence, under further assumptions on E, the strong and approximate convexity properties of (E,t)-convex functions can be strengthened.
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Acta Mathematica Hungarica
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