Temat: semiconcavity - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Paraconvex, but not strongly, Takagi functions
Autorzy:: Tabor, J.
Powiązania:: https://bibliotekanauki.pl/articles/205684.pdf
Data publikacji:: 2012
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: paraconvexity
strongly paraconvex function
semiconcavity
Takagi function
Opis:: There is an important open problem in the theory of approximate convexity whether every paraconvex function on a bounded interval is strongly paraconvex. Our aim is to show that this is not the case. To do this we need the following generalization of Takagi function. For a sequence a = (a_i)_i∈N ⊂ R₊ we consider Takagi-like function of the form T(a)(x) := ∑ ^∞ _i=1 a_idist(x, ¹₂^i-1Z) for x ∈ R. We give convenient conditions for verification whether T(a) is paraconvex or strongly paraconvex. This enables us to construct a class of paraconvex functions which are not strongly paraconvex.
Źródło:: Control and Cybernetics; 2012, 41, 3; 545-559
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Generalized approximate midconvexity
Autorzy:: Tabor, J.
Powiązania:: https://bibliotekanauki.pl/articles/969650.pdf
Data publikacji:: 2009
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: approximately midconvex function
convexity
paraconvexity
semiconcavity
Opis:: 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.
Źródło:: Control and Cybernetics; 2009, 38, 3; 655-669
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

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