Sever Silvestru Dragomir
In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and Renyi's entropy mappings are also given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They represents a refinement of these inequalities in the case of convex/concave functions with numerous applications in Theory of Means and Probability and Statistics.
In this paper, we give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point.
The theory and applications of dynamic derivatives on time scales has recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-$α$ derivatives which are a linear combination of delta and nabla dynamic derivatives on time scales. We prove a generalized version of Jensen's inequality on time scales via the diamond-$α$ integral and present some corollaries, including Hölder's and Minkowski's diamond-$α$ integral inequalities.
We extend Dragomir's refinement of Jensen's inequality from the dicrete to the general case, identifying the equality conditions.
Jensen convex functions and doubly stochastic matrices
本文研究双随机矩阵与 Jensen 凸性的关系，证明在适当线性代数条件下，相关矩阵型函数不等式可推出 f 为 Jensen 凸，并说明凸函数对任意阶双随机矩阵均满足该不等式。
Jensen's inequality for partial traces in von Neumann algebras
本文在半有限冯·诺依曼代数中证明了部分追踪的詹森不等式，并扩展至一般冯·诺依曼代数框架。
Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work we prove some new Jensen-type inequalities for $m$-convex functions, and we apply them to generalized Riemann-Liouville-type integral operators. It is remarkable that, if we consider $m=1$, we obtain new inequalities for convex functions.
It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as well. In other words, the arithmetic mean and the Jensen inequality (as a convexity property) are both reducible. Motivated by this phenomenon, we investigate this property concerning more general means and convexity notions. We introduce a wide class of means which generalize the well-known means for arbitrary linear spaces and enjoy a so-called reducibility …
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 functions. As their consequences, we derive the refinements for Young's inequality and Jensen's inequality. In addition, the operator Jensen's type inequality is also developed for conditioned two functions. Utilizing these new inequalities, we investigate the operator inequalities related to the relative operator entropy.
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 extended idea of convexity to the class of strongly convex functions. We also obtaine upper bound for Sherman's inequality, so called the converse Sherman inequality, and as easy consequences we get Jensen's as well as majorization inequality and their conversions for strongly convex functions. Obtained results are stronger versions for analogous results for c…
We present both necessary and sufficient conditions to the convex closed shape $X$ such that the inequality $$ \frac{1}{|X|} \int_X f(x)\:dx \le \frac{1}{|\partial X|} \int_{\partial X} f(x)\:dx$$ is valid for every convex function $f \colon X \to \mathbb{R}$ ($\partial X$ stands for the boundary of $X$). It is proved that this inequality holds if $X$ is (i) an $n$-dimensional parallelotope, (ii) an $n$-dimensional ball, (iii) a convex polytope having an inscribed sphere (tangent to all its facets) with center in the center of mass of $\partial X$.
Landau's converse to H\" older's inequality
本文证明兰道对赫尔德不等式的逆命题，并进一步研究希尔伯特不等式框架下的相关问题。
We prove two inequalities for the Mittag-Leffler function, namely that the function $\log E_α(x^α)$ is sub-additive for $0<α<1,$ and super-additive for $α>1.$ These assertions follow from two new binomial inequalities, one of which is a converse to the neo-classical inequality. The proofs use a generalization of the binomial theorem due to Hara and Hino (Bull. London Math. Soc. 2010). For $0<α<2,$ we also show that $E_α(x^α)$ is log-concave resp. log-convex, using analytic as well as probabilistic arguments.
In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.
This paper discusses the approximation by de la Vallée Poussin means $V_nf$ on the unit sphere. Especially, the lower bound of approximation is studied. As a main result, the strong converse inequality for the means is established. Namely, it is proved that there are constants $C_1$ and $C_2$ such that \begin{eqnarray*} C_1ω(f,\frac{1}{\sqrt n})_p \leq \|V_{n}f-f\|_p \leq C_2ω(f,\frac{1}{\sqrt n})_p \end{eqnarray*} for any $p$-th Lebesgue integrable or continuous function $f$ defined on the sphere, where $ω(f,t)_p$ is the modulus of smoothness of $f$.
Generalized Jensen's inequality motivated from thermodynamics
本文受热力学定律启发提出并证明广义 Jensen 不等式，统一导出加权 AM-GM-HM 等不等式，同时证明多物体热平衡温度的唯一性与过程的自发性。
Estimates for approximately Jensen convex functions
本文研究带误差函数 φ 的近似 Jensen 凸函数，建立其对任意有理凸组合的显式凸性误差估计，并证明相应无穷级数收敛且在有理参数下可化为有限和。
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 generalized Hermite-Hadamard inequality. Furthermore,some applications are given.
For every given real value of the ratio $μ:=A_X/G_X>1$ of the arithmetic and geometric means of a positive random variable $X$ and every real $v>0$, exact upper bounds on the right- and left-tail probabilities $\mathsf{P}(X/G_X\ge v)$ and $\mathsf{P}(X/G_X\le v)$ are obtained, in terms of $μ$ and $v$. In particular, these bounds imply that $X/G_X\to1$ in probability as $A_X/G_X\downarrow1$. Such a result may be viewed as a converse to a reverse Jensen inequality for the strictly concave function $f=\ln$, whereas the well-known Cantelli and Chebyshev inequalities may be viewed as converses to a…
In this paper we investigate continuity properties of functions $f:\mathbb{R}_+\to\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity inequality $$ f\big(H_p(x,y)\big)\leq H_q(f(x),f(y)) \qquad(x,y>0), $$ where $H_p$ stands for the $p$th power (or Hölder) mean. One of the main results shows that there exist discontinuous multiplicative functions that are $(p,p)$-Jensen convex for all positive rational number $p$. A counterpart of this result states that if $f$ is $(p,p)$-Jensen convex for all $p\in P\subseteq\mathbb{R}_+$, where $P$ is a set of positive Lebesgue measure, then $f$ must be c…
In this work, we introduce the class of $h$-${\rm{MN}}$-convex functions by generalizing the concept of ${\rm{MN}}$-convexity and combining it with $h$-convexity. Namely, Let $I,J$ be two intervals subset of $\left(0,\infty\right)$ such that $\left(0,1\right)\subseteq J$ and $\left[a,b\right]\subseteq I$. Consider a non-negative function $h: (0,\infty)\to \left(0,\infty\right)$ and let ${\rm{M}}:\left[0,1\right]\to \left[a,b\right] $ $(0<a<b)$ be a Mean function given by ${\rm{\rm{M}}}\left(t\right)={\rm{\rm{M}}}\left( {h(t);a,b} \right)$; where by ${\rm{\rm{M}}}\left( {h(t);a,b} \right)$ we m…
On Type IV Superorthogonality
该研究针对IV型超正交性，证明了向量值情形下的正向与反向不等式，且所得反向不等式在标量情形下也为新结论。
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 Hardy-Littlewood-Pólya theorem of majorization is proved and new insight is given into the problem of risk aversion in mathematical finance.
We present a tight parametrical Hermite-Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value of convex function than the classical one. Our inequality becomes equality not only with affine functions, but also with a family of V-shaped curves determined by the parameter. The residual (error) of this inequality is strictly smaller than in the classical Hermite-Hadamard inequality under any probability measure and with all non-affine convex functions. In the framework of Karamata's theorem on the inequalities with convex functions, w…
A convexity-type functional inequality with infinite convex combinations
本文证明了在 $d$ 维欧几里得空间非空凸子集上，满足无穷凸组合凸性型泛函不等式的下有界函数必为凸函数，并利用 Jensen 不等式的概率版本对已有结果给出了替代证明。
In the paper, the authors review several refinements of Young's integral inequality via several mean value theorems, such as Lagrange's and Taylor's mean value theorems of Lagrange's and Cauchy's type remainders, and via several fundamental inequalities, such as Čebyšev's integral inequality, Hermite--Hadamard's type integral inequalities, Hölder's integral inequality, and Jensen's discrete and integral inequalities, in terms of higher order derivatives and their norms, survey several applications of several refinements of Young's integral inequality, and further refine Young's integral inequa…
A short proof of an identity related to Type IV superorthogonality
本研究给出IV型超正交相关代数恒等式的更简短有力证明，得到正向不等式形式常数的最优阶数，恢复多个经典不等式常数的最优阶，还引入IV型超正交变体并证明其下的逆向不等式。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。