Sharp estimates of the curvature of some free boundaries in two dimensions.
Sharpening of Jordan's inequality and its applications.
Some Completely Monotonic Properties for the (p, g)-Gamma Function
MSC 2010: 33B15, 26A51, 26A48
Some considerations on the monotonicity property of power means.
Some inequalities connected with an approximate integration.
Some localization theorems using a majorization technique.
Some matrix inequalities of London type
Some New Multidimensional Hardy-type Inequalities With Kernels Via Convexity
Some remarks on a paper by A. McD. Mercer: “Polynomials and convex sequence inequalities” [JIPAM. J. Inequal. Pure Appl. Math. 6, 2005, no. 1, Paper No. 8, 4p., electronic only].
Some remarks on Hadamard's inequalities for convex functions.
Some remarks on s-convex functions.
Some weighted multidimensional Berwald, Thunsdorff and Borell inequalities.
Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities
Let ϕ be an arbitrary bijection of . We prove that if the two-place function is subadditive in then must be a convex homeomorphism of . This is a partial converse of Mulholland’s inequality. Some new properties of subadditive bijections of are also given. We apply the above results to obtain several converses of Minkowski’s inequality.
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 dual of the cone of all convex functions on a vector space.
The Dual of the Cone of All Convex Functions on a Vector Space. (Short Communication).
The extension of majorization inequalities within the framework of relative convexity.
The Extremal Convex Functions.
The Hardy-Landau-Littlewood inequalities with less smoothness.
The power mean and the logarithmic mean.