# 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.

## 9 Citations

### Reverses of Jensen’s Integral Inequality and Applications: A Survey of Recent Results

- Mathematics
- 2018

Several new reverses of the celebrated Jensen’s inequality for convex functions and Lebesgue integral on measurable spaces are surveyed. Applications for weighted discrete means, to Holder…

### A Survey of Reverse Inequalities for f-Divergence Measure in Information Theory

- Mathematics, Computer Science
- 2015

In this paper we survey some discrete inequalities for the f-divergence measure in Information Theory by the use of recent reverses of the celebrated Jensen’s inequality. Applications in connection…

### Inequalities of Jensen Type for φ-Convex Functions

- Mathematics
- 2015

Abstract Some inequalities of Jensen type for φ-convex functions defined on real intervals are given.

### Weighted Reverse Inequalities of Jensen Type for Functions of Selfadjoint Operators

- Mathematics
- 2016

On making use of the representation in terms of the Riemann-Stieltjes integral of spectral families for selfadjoint operators in Hilbert spaces, we establish here some weighted reverse inequalities…

### Inequality for power series with nonnegative coefficients and applications

- Mathematics
- 2015

Abstract We establish in this paper some Jensen’s type inequalities for functions defined by power series with nonnegative coefficients. Applications for functions of selfadjoint operators on complex…

### Recent Developments of Discrete Inequalities for Convex Functions Defined on Linear Spaces with Applications

- Mathematics, Computer Science
- 2018

This paper surveys some recent discrete inequalities for functions defined on convex subsets of general linear spaces and establishes several bounds for the mean f-deviation of an n-tuple of vectors as well as for the f-divergence of ann -t tuple of vectors given a discrete probability distribution.

### Two Points Taylor’s Type Representations with Integral Remainders

- MathematicsDifferential and Integral Inequalities
- 2019

In this chapter we establish some two points Taylor’s type representations with integral remainders and apply them for the logarithmic and exponential functions. Some inequalities for weighted…

### LOWER AND UPPER BOUNDS FOR THE PERTURBED JENSENS GAP OF CONVEX FUNCTIONS

- Mathematics
- 2020

For simplicity of notation we write everywhere in the sequel R wd instead of R w (t) d (t) : In order to provide a reverse of the celebrated Jensens integral inequality for convex functions, the…

### Arikan meets Shannon: Polar codes with near-optimal convergence to channel capacity

- Computer ScienceIEEE Transactions on Information Theory
- 2022

The converse theorem shows extreme unpredictability of even a single message bit for random coding at rates slightly above capacity for binary-input memoryless symmetric channels with Shannon capacity I(W) resolving a central theoretical challenge associated with the attainment of Shannon capacity.

## References

SHOWING 1-10 OF 46 REFERENCES

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

- Mathematics
- 2001

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

- Mathematics
- 2007

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.

- Mathematics
- 2001

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

- Mathematics
- 2008

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…

### AN EXTENSION OF CHEBYSHEVS INEQUALITY AND ITS CONNECTION WITH JENSENS INEQUALITY

- Mathematics
- 2008

The aim of this paper is to show that Jensens Inequality and an extension of Chebyshevs 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

- Mathematics
- 2002

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

- Mathematics
- 1997

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

- Computer Science
- 1995

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

- Computer ScienceIEEE Trans. Inf. Theory
- 1991

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.