Strengthening of strong and approximate convexity

J. Makó, Z. S. Páles

Research output: Contribution to journalArticle

7 Citations (Scopus)


Let X be a real linear space and D {subset double equals} X be a nonempty convex subset. Given an error function E:[0,1]×(D-D)→ℝ∪{+∞} and an element t ∈]0, 1[, a function f:D→ℝ is called (E,t)-convex if f(tx+(1-t)y)≦ tf(x)+(1-t)f(y)+E(t,x-y) for all x,y∈D. 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, As a consequence, under further assumptions on E, the strong and approximate convexity properties of (E,t)-convex functions can be strengthened.

Original languageEnglish
Pages (from-to)78-91
Number of pages14
JournalActa Mathematica Hungarica
Issue number1-2
Publication statusPublished - Jul 1 2011


  • (E,t)-convexity
  • 39B12
  • 39B22
  • approximate and strong convexity

ASJC Scopus subject areas

  • Mathematics(all)

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