A Refinement and a divided difference reverse of Jensen's inequality with applications

@inproceedings{Dragomir2016ARA,
  title={A Refinement and a divided difference reverse of Jensen's inequality with applications},
  author={Sever Silvestru Dragomir},
  year={2016}
}
A renement and a new sharp reverse of Jensen's inequality for convex functions in terms of divided diferences is obtained. Applications for means, the Holder inequality and for f -divergence measures in information theory are also provided. 

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References

SHOWING 1-10 OF 46 REFERENCES

ON A REVERSE OF JESSEN ’ S INEQUALITY FOR ISOTONIC LINEAR FUNCTIONALS

A reverse of Jessen’s inequality and its version for m − Ψ−convex andM − Ψ−convex functions are obtained. Some applications for particular cases are also pointed out.

A refinement of the Gr"{u}ss inequality and applications

A sharp refinement of the Gr"{u}ss inequality in the general setting of measurable spaces and abstract Lebesgue integrals is proven. Some consequential particular inequalities are mentioned.

An extension of Chebyshev's inequality and its connection with Jensen's inequality.

The well known fact that the derivative and the integral are inverse each other has a lot of interesting consequences, one of them being the duality between convexity and monotonicity. The purpose of

BOUNDS FOR THE DEVIATION OF A FUNCTION FROM THE CHORD GENERATED BY ITS EXTREMITIES

Sharp bounds for the deviation of a real-valued function f defined on a compact interval [ a , b ] to the chord generated by its end points ( a , f ( a )) and ( b , f ( b )) under various assumptions

Some converse of Jensen's inequality and applications

AN EXTENSION OF CHEBYSHEVS INEQUALITY AND ITS CONNECTION WITH JENSENS INEQUALITY

The aim of this paper is to show that Jensen’s Inequality and an extension of Chebyshev’s Inequality complement one another, so that they both can be formulated in a pairing form, including a second

A NOTE ON THE PERTURBED TRAPEZOID INEQUALITY

In this paper, we utilize a variant of the Gruss inequality to obtain some new per- turbed trapezoid inequalities. We improve the error bound of the trapezoid rule in numerical integration in some

On Information and Sufficiency

The information deviation between any two finite measures cannot be increased by any statistical operations (Markov morphisms). It is invarient if and only if the morphism is sufficient for these two

A generalization of lin divergence and the derivation of a new information divergence

TLDR
Based on Lin's method of constructing the divergence, a new divergence called Hermite-Hadamard divergence is introduced and the property of the proposed divergence, as well as its relation to Lin's inequality, are discussed.

Divergence measures based on the Shannon entropy

TLDR
A novel class of information-theoretic divergence measures based on the Shannon entropy is introduced, which do not require the condition of absolute continuity to be satisfied by the probability distributions involved and are established in terms of bounds.