Jensen Type Inequalities Involving Homogeneous Polynomials

Jensen Polynomials and the Turan and Laguerre Inequalities

Inequalities of Jensen-pečarić-svrtan-fan Type

By using the theory of majorization, the following inequalities of Jensen-PečarićSvrtan-Fan type are established: Let I be an interval, f : I → R and t ∈ I, x, a, b ∈ I. If a1 ≤ · · · ≤ an ≤ bn ≤ · · · ≤ b1, a1 +b1 ≤ · · · ≤ an +bn; f(t) > 0, f ′(t) > 0, f ′′(t) > 0, f ′′′(t) < 0 for any t ∈ I, then f(A(a)) f(A(b)) = fn,n(a) fn,n(b) ≤ · · · ≤ fk+1,n(a) fk+1,n(b) ≤ fk,n(a) fk,n(b) ≤ · · · ≤ f1,n...

IteratedHardy-type inequalities involving suprema

In this paper the complete solution of the restricted inequalities for supremal operators are given. The boundedness of the composition of supremal operators with the Hardy and Copson operators in weighted Lebesgue spaces are characterized.

Jensen-Ostrowski type inequalities and applications for f-divergence measures

In this paper, we provide inequalities of Jensen-Ostrowski type, by investigating the magnitude of the quantity ∫ Ω (f ◦ g) dμ− f(ζ)− ∫ Ω (g − ζ)f ′ ◦ g dμ+ 1 2 λ ∫ Ω (g − ζ) dμ, for various assumptions on the absolutely continuous function f : [a, b] → C, ζ ∈ [a, b], λ ∈ C and a μ-measurable function g on Ω. Special cases are considered to provide some inequalities of Jensen type, as well as O...

Ostrowski and Jensen Type Inequalities for Higher Derivatives with Applications

We consider inequalities which incorporate both Jensen and Ostrowski type inequalities for functions with absolutely continuous n-th derivative. We provide applications of these inequalities for divergence measures. In particular, we obtain inequalities involving higher order χ-divergence.