Related papers: More on Jensen functional and convexity
We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables
In this work, new inequalities connected with the Steffensen's integral inequality for s-convex functions are proved
Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the…
In this paper, one new classes of convex functions which is called MT-convex functions are given. We also establish some Hadamard-type inequalities.
In this paper, we describe s-logarithmically convex functions in the first and second sense which are connected with the ordinary logatihmic convex and s-convex in the first and second sense. Afterwards, some new inequalities related to…
We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.
Given a function $f$ defined on a nonempty and convex subset of the $d$-dimensional Euclidean space, we prove that if $f$ is bounded from below and it satisfies a convexity-type functional inequality with infinite convex combinations, then…
We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
In this paper, we introduce new technique for determining some necessary and sufficient conditions of the normalized Bessel functions $j_{\nu}$, normalized Struve functions $h_{\nu}$ and normalized Lommel functions $s_{\mu,\nu}$ of the…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the…
This paper deals with more refinements of inequalities related to deviations from Mean Value involving superquadratic and uniformly convex functions.
We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…
We investigate how the type of Convexity of the Core function affects the Csisz\'{a}r $f$-divergence functional. A general treatment for the type of convexity has been considered and the associated perspective functions have been studied.…
In this paper, two new lemmas are proved and inequalities are established for co-ordinated convex functions and co-ordinated s-convex functions.
In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…
We have recently established some integral inequalities for convex functions via the Hermite-Hadamard's inequalities. In continuation here, we also establish some interesting new integral inequalities for convex functions via the…
The notion of Ces\`aro stable function is generalized by introducing Ces\`aro mean of type $(b-1;c)$ which give rise to a new concept of generalized Ces\`aro stable function. As an application of generalized Ces\`aro stable functions we…