Jensen and Ostrowski type inequalities for general Lebesgue integral with applications

New Jensen and Ostrowski Type Inequalities for General Lebesgue Integral with Applications

Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.

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.

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...

Some General Ostrowski Type Inequalities

A new general Ostrowski type inequality for functions whose (n − 1)th derivatives are continuous functions of bounded variation is established. Some special cases are discussed.

Some generalized Ostrowski-Grüss type integral inequalities