Abstract
Some inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral of differentiable functions whose derivatives in absolute value are h-convex are obtained. Applications for f-divergence measure are provided as well.
Highlights
Let (Ω, A, μ) be a measurable space consisting of a set Ω, a σ-algebra A of parts of Ω and a countably additive and positive measure μ on A with values in R ∪ {∞}
Motivated by the above results, in this paper we provide more upper bounds for the quantity
The above concept can be extended for functions Φ : C ⊆ X → [0, ∞) where C is a convex subset of the real or complex linear space X and the inequality (2.10) is satisfied for any vectors x, y ∈ C and t ∈ (0, 1)
Summary
Let (Ω, A, μ) be a measurable space consisting of a set Ω, a σ-algebra A of parts of Ω and a countably additive and positive measure μ on A with values in R ∪ {∞}. In order to provide a reverse of the celebrated Jensen’s integral inequality for convex functions, S. Let Φ : [m, M ] → R be a differentiable convex function on (m, M ).
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