The A. M. -G. M. inequality as a rearrangement inequality.
The approximation of a polynomial's measure, with applications towards Jensen's theorem.
The arithmetic-algebraic mean inequality via symmetric means.
The best constant for Carleman's inequality of finite type.
The best constant of Sobolev inequality corresponding to clamped boundary value problem.
The best lower bound depended on two fixed variables for Jensen's inequality with ordered variables.
The best possibility of the bound for the Kantorovich inequality and some remarks.
The Brascamp–Lieb inequalities: recent developments
We discuss recent progress on issues surrounding the Brascamp–Lieb inequalities.
The Choquet integral as Lebesgue integral and related inequalities
The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee the validity of the discussed inequalities are given. Moreover, the comonotonicity of the considered functions...
The construction of some means.
The converse of the Hölder inequality and its generalizations
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 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...
The counterpart of Fan's inequality and its related results.
The discrete version of Ostrowski's inequality in normed linear spaces.
The extension of a cyclic inequality to the symmetric form.
The extension of majorization inequalities within the framework of relative convexity.
The extension of Montgomery identity via Fink identity with applications.
The generalizations of Hilbert's inequality.
The generalized Heron mean and its dual form.
The Hardy inequality with one negative parameter.
The Hermite-Hadamard type inequality of GA-convex functions and its application.