2 research outputs found
How type of Convexity of the Core function affects the Csisz\'{a}r -divergence functional
We investigate how the type of Convexity of the Core function affects the
Csisz\'{a}r -divergence functional. A general treatment for the type of
convexity has been considered and the associated perspective functions have
been studied. In particular, it has been shown that when the core function is
\rm{MN}-convex, then the associated perspective function is jointly
\rm{MN}-convex if the two scalar mean \rm{M} and \rm{N} are the same. In the
case where , we study the type of convexity of the
perspective function. As an application, we prove that the \textit{Hellinger
distance} is jointly \rm{GG}-convex. As further applications, the matrix Jensen
inequality has been developed for the perspective functions under different
kinds of convexity
Some inequalities on -convex functions
In this paper, we state some characterizations of -convex function is
defined on a convex set in a linear space. By doing so, we extend the
Jensen-Mercer inequality for -convex function. We will also define
-convex function for operators on a Hilbert space and present the operator
version of the Jensen-Mercer inequality. Lastly, we propound the complementary
inequality of Jensen's inequality for -convex functions