Related papers: Affine and Functional Form of Jensen's Inequalitiy…
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
We establish what we consider to be the definitive versions of Jensen's operator inequality and Jensen's trace inequality for functions defined on an interval. This is accomplished by the introduction of genuine non-commutative convex…
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 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…
In this paper, we state some characterizations of $h$-convex function is defined on a convex set in a linear space. By doing so, we extend the Jensen-Mercer inequality for $h$-convex function. We will also define $h$-convex function for…
In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen's type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's…
Jensen's trace inequality is established for every multivariable, convex function and every trace or trace-like functional on a C*-algebra.
It is well known that the traditional Jensen inequality is proved by lower bounding the given convex function, $f(x)$, by the tangential affine function that passes through the point $(E\{X\},f(E\{X\}))$, where $E\{X\}$ is the expectation…
Motivated by some recently established operator Jensen-type inequalities related to a usual convexity, in the present paper we derive several more accurate operator Jensen-type inequalities for certain subclasses of convex functions. More…
In this work, new inequalities connected with the Steffensen's integral inequality for s-convex functions are proved
Problems pointwise estimates from above functions or its averages often arise in the function theory under known integral restrictions on the growth of this function. We offer an approach to such problems based on the integral Jensen's…
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.
In the paper, we introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen inequality and…
We develop a new framework for the Jensen-type inequalities that allows us to deal with functions not necessarily convex and Borel measures not necessarily positive.
In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main result relies on the linear interpolation of a convex function. As a consequence,…
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type…
The well known Jensen inequality, holds true for every convex functions. However, we found that it is possible to apply it to some problems related to nonconvex functions for which Jensen's inequality holds true locally. Having considered a…
Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using…