# SHARP BOUNDS FOR THE JENSEN DIVERGENCE WITH APPLICATIONS

## Related Articles

- SOME REVERSES OF THE JENSEN INEQUALITY WITH APPLICATIONS. DRAGOMIR, S. S. // Bulletin of the Australian Mathematical Society;Apr2013, Vol. 87 Issue 2, p177
Two new reverses of the celebrated Jensenâ€™s inequality for convex functions in the general setting of the Lebesgue integral, with applications to means, HÃ¶lderâ€™s inequality and $f$-divergence measures in information theory, are given.

- SUPERADDITIVITY OF THE JENSEN INTEGRAL INEQUALITY WITH APPLICATIONS. DRAGOMIR, S. S. // Miskolc Mathematical Notes;2012, Vol. 13 Issue 2, p303
The superadditivity and monotonicity of two functionals associated to the celebrated Jensen's integral inequality for convex functions with applications for HÃ¶lder's inequality and f -divergence measures in information theory are given.

- A Novel Nonparametric Distance Estimator for Densities with Error Bounds. Carvalho, Alexandre R. F.; Tavares, João Manuel R. S.; Principe, Jose C. // Entropy;Jun2013, Vol. 15 Issue 6, p1609
The use of a metric to assess distance between probability densities is an important practical problem. In this work, a particular metric induced by an a-divergence is studied. The Hellinger metric can be interpreted as a particular case within the framework of generalized Tsallis divergences...

- ELLIPTIC EXTENSIONS IN THE DISK WITH OPERATORS IN DIVERGENCE FORM. ARENA, ORAZIO; GIANNOTTI, CRISTINA // Bulletin of the Australian Mathematical Society;Aug2013, Vol. 88 Issue 1, p51
Let $\varphi _0$ and $\varphi _1$ be regular functions on the boundary $\partial D$ of the unit disk $D$ in $\mathbb {R}^2$, such that $\int _{0}^{2\pi }\varphi _1\,d\theta =0$ and $\int _{0}^{2\pi }\sin \theta (\varphi _1-\varphi _0)\,d\theta =0$. It is proved that there exist a linear...

- PARABOLIC SQUARE FUNCTIONS AND CALORIC MEASURE. RIVERA-NORIEGA, JORGE // Communications in Mathematical Analysis;2012, Vol. 13 Issue 1, p64
We prove estimates for certain square functions of solutions to divergence form linear parabolic equations. The estimates are related to singularity and mutual absolute continuity of caloric measure with respect to surface measure of non-cylindrical domains. The square functions and the results...

- On Barycentric Interpolation. II (GrÃ¼nwald-Marcinkiewicz type Theorems). Horváth, Á.; Vértesi, P. // Acta Mathematica Hungarica;Feb2016, Vol. 148 Issue 1, p147
GrÃ¼nwald-Marcinkiewicz type theorems with respect to barycentric Lagrange interpolation based on equidistant and Chebyshev node-sytems in [-1, 1] are proved. It turns out that the results are very similar to the ones known for the classical Lagrange interpolation.

- Error terms for Jensen's and Levinson's Inequalities. MERCER, PETER R.; SESAY, ALLAN A. // Mathematical Gazette;Jul2013, Vol. 97 Issue 539, p277
The article discusses the developments in the field of mathematics. It focuses on the error terms for the Jensen's Inequality and Levinson's Inequality. It examines the claim that a function, f, defined on [a, b] is convex when for any x, y âˆˆ [a, b], f (tx + (1 - t)y) â‰¤ tf (x) + (1 -...

- Some new estimates of the 'Jensen gap'. Abramovich, Shoshana; Persson, Lars-Erik // Journal of Inequalities & Applications;2/1/2016, Vol. 2016 Issue 1, p1
Let $( \mu,\Omega ) $ be a probability measure space. We consider the so-called 'Jensen gap' for some classes of functions Ï†. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when Ï† has a Taylor expansion is treated and...

- Exponential convexity for Jensen's inequality for norms. Jakšetić, Julije; Naeem, Rishi; Pečarić, Josip // Journal of Inequalities & Applications;2/12/2016, Vol. 2016 Issue 1, p1
In this paper, we investigate n-exponential convexity and log-convexity using the positive functional defined as the difference of the left-hand side and right-hand side of the inequality from (PeÄariÄ‡ and JaniÄ‡ in Facta Univ., Ser. Math. Inform. 3:39-42, ). We also give mean value...