Generalized approximate midconvexity

• Autorzy: Tabor J. , Tabor J.
• Języki publikacji: EN

Abstrakty

EN

Let X be a normed space and V ⊂ X a convex set with nonempty interior. Let α : [0, ∞) → [0, ∞) be a given nondecreasing function. A function ƒ : V → R is α(⋅)-midconvex if ƒ [wzór]. In this paper we study α(⋅)-midconvex functions. Using a version of Bernstein-Doetsch theorem we prove that if ƒ is α(⋅)-midconvex and locally bounded from above at every point then ƒ(rx + (1 - r)y) ≤ rƒ(x) + (1 - r)ƒ(y) + Pα(r, ¦¦x - y¦¦) for x,y ∈ V and r ∈ [0,1], where Pα : [0,1] x [0,∞) → [0,∞) is a specific function dependent on α. We obtain three different estimations of Pα. This enables us to generalize some results concerning paraconvex and semiconcave functions.

Słowa kluczowe

EN

approximately midconvex function; convexity; paraconvexity; semiconcavity

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 3
• Strony: 655--669
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Tabor J.

autor

Tabor J.

• Institute of Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, te,

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