Temat: inequality measure - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities
Autorzy:: Matkowski, J.
Świątkowski, T.
Powiązania:: https://bibliotekanauki.pl/articles/1208624.pdf
Data publikacji:: 1993
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: subadditive function
homeomorphisms of $ℝ_+$
Mulholland's inequality
convex function
iteration
measure space
the converse of Minkowski's inequality
Opis:: Let ϕ be an arbitrary bijection of $ℝ_+$. We prove that if the two-place function $ϕ^{-1}[ϕ (s)+ϕ (t)]$ is subadditive in $ℝ^2_+$ then $ϕ $ must be a convex homeomorphism of $ℝ_+$. This is a partial converse of Mulholland's inequality. Some new properties of subadditive bijections of $ℝ_+$ are also given. We apply the above results to obtain several converses of Minkowski's inequality.
Źródło:: Fundamenta Mathematicae; 1993, 143, 1; 75-85
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: The converse of the Hölder inequality and its generalizations
Autorzy:: Matkowski, Janusz
Powiązania:: https://bibliotekanauki.pl/articles/1290537.pdf
Data publikacji:: 1994
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: measure space
integrable step functions
conjugate functions
a converse of Hölder inequality
subadditive function
convex function
generalized Hölder-Minkowski inequality
Opis:: Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if $ʃ_Ω xydμ ≤ ϕ^{-1} (\int_{Ω} ϕ∘x dμ) ψ^{-1} (\int_{Ω} ψ∘x dμ)$ for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then there exist some broad classes of nonpower bijections ϕ and ψ such that the above inequality holds true. A general inequality which contains integral Hölder and Minkowski inequalities as very special cases is also given.
Źródło:: Studia Mathematica; 1994, 109, 2; 171-182
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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