# 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…

### 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

A constructive version of Shannon’s theorem with near-optimal convergence to capacity as a function of the block length is resolved, which resolves a central theoretical challenge associated with the attainment of Shannon capacity.

### 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…

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