Results 21 to 30 of about 950,431 (295)
Optimal evaluations for the S\'{a}ndor-Yang mean by power mean [PDF]
, 2015 In this paper, we prove that the double inequality $M_{p}(a,b) 0$ with $a\neq b$ if and only if $p\leq 4\log 2/(4+2\log 2-\pi)=1.2351\cdots$ and $q\geq 4/3$, where $% M_{r}(a,b)=[(a^{r}+b^{r})/2]^{1/r}$ $(r\neq 0)$ and $M_{0}(a,b)=\sqrt{ab}$ is the $r$th
Zhen-Hang Yang, Y. Chu
semanticscholar +1 more source
AIMS Mathematics, 2022 In this paper, we introduce the class of generalized strongly convex functions using Raina's function. We derive two new general auxiliary results involving first and second order (p,q)-differentiable functions and Raina's function.
Miguel Vivas-Cortez +4 more
doaj +1 more source
Some new Ostrowski’s Inequalities for Functions whose nth Derivatives are Logarithmically Convex
Annales Mathematicae Silesianae, 2018 Some new Ostrowski’s inequalities for functions whose nthderivative are logarithmically convex are established.
Meftah Badreddine
doaj +1 more source
AIMS Mathematics, 2022 Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored.
Jamshed Nasir +4 more
doaj +1 more source
On a result of Cartwright and Field
Journal of Inequalities and Applications, 2018 Let Mn,r=(∑i=1nqixir)1r $M_{n,r}=(\sum_{i=1}^{n}q_{i}x_{i}^{r})^{\frac{1}{r}}$, r≠0 $r\neq 0$, and Mn,0=limr→0Mn,r $M_{n,0}= \lim_{r \rightarrow 0}M_{n,r}$ be the weighted power means of n non-negative numbers xi $x_{i}$, 1≤i≤n $1 \leq i \leq n$, with qi>
Peng Gao
doaj +1 more source
Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function [PDF]
, 2005 In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in R^n belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors over which the
Baraud, Yannick +2 more
core +4 more sources
On matrix inequalities between the power means: Counterexamples
Linear Algebra and its Applications, 2013 We prove that the known sufficient conditions on the real parameters $(p,q)$ for which the matrix power mean inequality $((A^p+B^p)/2)^{1/p}\le((A^q+B^q)/2)^{1/q}$ holds for every pair of matrices $A,B>0$ are indeed best possible. The proof proceeds by constructing $2\times2$ counterexamples. The best possible conditions on $(p,q)$ for which $ (A^p)
Audenaert, Koenraad M. R., Hiai, Fumio
openaire +2 more sources
The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the Hölder Inequality
Symmetry, 2018 In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the
Yongtao Li, Xianming Gu, Jianxing Zhao
semanticscholar +1 more source
Optimal power mean bounds for Yang mean
Journal of Inequalities and Applications, 2014 In this paper, we prove that the double inequality Mp(a,b)
Zhen-Hang Yang, Li-Min Wu, Y. Chu
semanticscholar +2 more sources
FORMATION OF VERSIONS OF SOME DYNAMIC INEQUALITIES UNIFIED ON TIME SCALE CALCULUS
Ural Mathematical Journal, 2018 The aim of this paper is to present some comprehensive and extended versions of classical inequalities such as Radon's Inequality, Bergström's Inequality, the weighted power mean inequality, Schlömilch's Inequality and Nesbitt's Inequality on time scale ...
Muhammad Jibril Shahab Sahir
doaj +1 more source