# SOME COMPANION INEQUALITIES TO JENSEN'S INEQUALITY

@article{Matic2000SOMECI, title={SOME COMPANION INEQUALITIES TO JENSEN'S INEQUALITY}, author={Marko Matic and Josip E. Pe{\vc}ari{\'c}}, journal={Mathematical Inequalities \& Applications}, year={2000}, pages={355-368} }

We prove a pair of general companion inequalities to Jensen's inequality in its discrete and integral form. Slater's inequality as well as the generalization of the counterpart to Jensen's inequality along with some further results are deduced from these general inequalities.

## 16 Citations

### On Some General Inequalities Related to Jensen’s Inequality

- Mathematics
- 2008

We present several general inequalities related to Jensen’s inequality and the Jensen-Steffensen inequality. Some recently proved results are obtained as special cases of these general inequalities.

### Generalizations of the Jensen-Steffensen and related inequalities

- Mathematics, Economics
- 2007

We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization…

### Refinements of some majorization type inequalities

- Mathematics
- 2013

In this paper, we prove reﬁnements of some companion inequalities to the Jensen inequality, namely Slater’s inequality and the inequalities obtained by Matic and Pecaric (2000). We also give…

### COMPANION INEQUALITIES TO JENSEN’S INEQUALITY FOR m-CONVEX AND (α, m)-CONVEX FUNCTIONS

- Mathematics
- 2006

General companion inequalities related to Jensen’s inequality for the classes of m-convex and(α, m)-convex functions are presented. We show how Jensen’s inequality for these two classes, as well as…

### Improvement of Jensen's Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications

- Mathematics
- 2012

In this paper, we prove some inequalities in terms of G^ateaux derivatives for convex functions dened on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give…

### Integral Inequalities Involving Strongly Convex Functions

- MathematicsJournal of Function Spaces
- 2018

We study the notions of strongly convex function as well as F-strongly convex function. We present here some new integral inequalities of Jensen’s type for these classes of functions. A refinement of…

### On Slater's Integral Inequality

- Mathematics
- 2011

In this paper we give a generalization of results given by Pecaric and Adil (2010). We use a log -convexity criterion and establish improvements and reverses of Slater’s and related inequalities.…

### The n-exponential convexity for majorization inequality for functions of two variables and related results

- Mathematics
- 2014

We apply the refined method of producing n -exponential convex functions of J. Pecaric and J. Peric to extend some known results on majorization type and related inequalities.

### Some Slater's Type Inequalities for Convex Functions Defined on Linear Spaces and Applications

- Mathematics
- 2012

Some inequalities of the Slater type for convex functions defined on general linear spaces are given. Applications for norm inequalities and f-divergence measures are also provided.

### Improvement and Reversion of Slater's Inequality and Related Results

- Mathematics
- 2010

We use an inequality given by Matić and Pečarić (2000) and obtain improvement and reverse of Slater's and related inequalities.

## References

SHOWING 1-6 OF 6 REFERENCES

### A counterpart of Jensen's discrete inequality for differentiable convex mappings and applications in information theory

- Mathematics, Computer Science
- 1996

### Classical and New Inequalities in Analysis

- Mathematics
- 1992

Preface. Organization of the Book. Notations. I. Convex Functions and Jensen's Inequality. II. Some Recent Results Involving Means. III. Bernoulli's Inequality. IV. Cauchy's and Related Inequalities.…

### Real and complex analysis

- Mathematics
- 1966

Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures…