Journal ArticleDOI
Functional inequality characterizing nonnegative concave functions in (0, ∞) k
TLDR
In this article, it was shown that for any function f : (0, ∞) → [0 ∞] satisfying the inequality f(s) + bf(t) ⩽ f(as + bt), s, t > 0, for somea andb such that 0 0).Abstract:
In the present note we prove that every functionf: (0, ∞) → [0, ∞) satisfying the inequalityaf(s) + bf(t) ⩽ f(as + bt), s, t > 0, for somea andb such that 0 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t ⩾ 0, and gives a positive answer to the question raised there.read more
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The converse theorem for Minkowski's inequality
TL;DR: In this article, it was shown that if there are A, B ϵ Σ such that 0 ϕ(t)=ϕ(1)t p, ψ(t))=ψ( 1)t 1 p, t>0), the assumption limt → 0 ψ (t) = 0 can be significantly weakened or, for some measure spaces, even omitted.
Journal ArticleDOI
Converse theorem for the Minkowski inequality
TL;DR: In this paper, it was shown that for all nonnegative μ-integrable simple functions x,y:Ω→R (where Ω(x) stands for the support of x), there exists a real p⩾1 such thatπ = t 1/p, φ(t)φφ(1)=φi(t)/p,i=1,2
Journal ArticleDOI
A converse of the hölder inequality theorem
TL;DR: In this article, it was shown that for all nonnegative μ-integrable simple functions x,y :Ω → R (where Ω(x) stands for the sup- port of x), there exists a real p > 1 such that ϕ1(t)
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Convex-like inequality, homogeneity, subadditivity, and a characterization of L p -norm
Janusz Matkowski,Marek Pycia +1 more
TL;DR: In this article, the functional inequality f(as +bt) af(s) +bf(t) was shown to be equivalent to the L p -norm for functions defined on cones in linear spaces.
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The converse of the Minkowski’s inequality theorem and its generalization
TL;DR: In this paper, a generalization of Minkowski's inequality theorem for normalized measure is presented, where the converse implication is shown to hold for all step functions from the Banach space.