We present a novel class of divergences induced by a smooth convex function called total Jensendivergences. Those total Jensen divergences are invariant by construction to rotations, a feature yieldingregularization of ordinary Jensen divergences by a conformal factor. We analyze the relationships be-tween this novel class of total Jensen divergences and the recently introduced tota...

Abstract: This paper proposes a radar target detection algorithm based on information geometry. In particular, the correlation of sample data is modeled as a Hermitian positive-definite (HPD) matrix. Moreover, a class of total Jensen–Bregman divergences, including the total Jensen square loss, the total Jensen log-determinant divergence, and the total Jensen von Neumann divergence, are proposed...

The main of this article are presenting generalized Opial type inequalities which will be defined as theOpial-Jensen inequality for convex function. Further, new given functionalsdefined with the help inequalities.

The aim of this paper is to derive some new generalized fractional analogues Mercer type inequalities, essentially using the convexity property functions and Raina’s function. We also discuss several special cases which show that our results are, an extent, unifying. In order illustrate significance results, we offer interesting applications means, error bounds, q-digamma functions.

The classical criterion of Jensen for the Riemann hypothesis is that all associated polynomials have only real zeros. We find a new version this criterion, using linear combinations Hermite polynomials, and show condition holds in many cases. Detailed asymptotic expansions are given required Taylor coefficients xi function at 1/2 as well related quantities. These results build on those recent p...

In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k, ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are generalization of some results that existed in the literature.

Given an arithmetic function a : N −→ R, one can associate a naturally defined, doubly infinite family of Jensen polynomials. Recent work of Griffin, Ono, Rolen, and Zagier shows that for certain families of functions a : N −→ R, the associated Jensen polynomials are eventually hyperbolic (i.e., eventually all of their roots are real). This work proves Chen, Jia, and Wang’s conjecture that the ...