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- Title
On conditionally δ-convex functions.
- Authors
Najdecki, Adam; Tabor, Jacek; Tabor, Józef
- Abstract
Let X be a real vector space, V a subset of X and δ ≧ 0 a given number. We say that f: V → ℝ is a conditionally δ-convex function if for each convex combination t1 υ1 + ... + t n υ n of elements of V such that t1 υ1 + ... + t n υ n ∈ V the following inequality holds true: We prove that f: V → ℝ is conditionally δ-convex if and only if there exists a convex function $$ \tilde f $$: conv V → [−∞, ∞) such that In case X = ℝ n some conditions equivalent to conditional δ-convexity are also presented.
- Subjects
VECTOR spaces; CONVEX functions; CONVEX domains; REAL variables; VECTOR analysis
- Publication
Acta Mathematica Hungarica, 2010, Vol 128, Issue 1/2, p131
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-010-9168-9