Results 11 to 20 of about 38,693 (157)
Optimal Inequalities for Power Means [PDF]
Journal of Applied Mathematics, 2012 We present the best possible power mean bounds for the product for any p > 0, α ∈ (0,1), and all a, b > 0 with a ≠ b. Here, Mp(a, b) is the pth power mean of two positive numbers a and b.
Li, Yong-Min +3 more
openaire +4 more sources
The optimization for the inequalities of power means [PDF]
Journal of Inequalities and Applications, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wen Jiajin, Wang Wan-Lan
openaire +3 more sources
An inequality for mixed power means [PDF]
Mathematical Inequalities & Applications, 1999 This paper contains a weighted version of a mixed power means inequality proved by \textit{B. Mond} and the reviewer [Austral. Math. Soc. Gaz. 23, No. 2, 67-70 (1996; Zbl 0866.26015)]. If \(s>r\) and if \(w= (w_1,w_2,\dots, w_n)\) satisfy \[ W_n w_k- W_k w_n>0\quad\text{for }2\leq k\leq n-1,\tag{\(*\)} \] where \(W_k:= \sum^k_{i=1} w_i\), then \[ m_{r ...
Tarnavas, Christos D. +1 more
openaire +2 more sources
Some Inequalities for Power Means; a Problem from “The Logarithmic Mean Revisited” [PDF]
The American Mathematical Monthly, 2023 We establish some inequalities comparing power means of two numbers with combinations of the arithmetic and geometric means. A conjecture from [Citation1] is confirmed.
openaire +1 more source
Two Sharp Inequalities for Power Mean, Geometric Mean, and Harmonic Mean [PDF]
Journal of Inequalities and Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xia Wei-Feng, Chu Yu-Ming
openaire +3 more sources
Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means [PDF]
Journal of Applied Mathematics, 2012 We prove that αH(a, b)+(1 − α)L(a, b) > M(1−4α)/3(a, b) for α ∈ (0, 1) and all a, b > 0 with a ≠ b if and only if α ∈ [1/4, 1) and αH(a, b)+(1 − α)L(a, b) < M(1−4α)/3(a, b) if and only if , and the parameter (1 − 4α)/3 is the best possible in either case.
Qian, Wei-Mao, Shen, Zhong-Hua
openaire +5 more sources
SEVERAL NEW INTEGRAL INEQUALITIES VIA K-RIEMANN–LIOUVILLE FRACTIONAL INTEGRALS OPERATORS
Проблемы анализа, 2021 The main objective of this paper is to establish several new integral inequalities including k-Riemann – Liouville fractional integrals for convex, s-Godunova – Levin convex functions, quasiconvex, η-quasi-convex.
S. I. Butt, B. Bayraktar, M. Umar
doaj +1 more source
Some Bullen-Simpson type inequalities for differentiable s-convex functions [PDF]
Mathematica MoravicaConvexity is one of the fundamental principles of analysis. Over the past few decades, many important inequalities have been established for different classes of convex functions.
Meftah Badreddine, Samoudi Sara
doaj +1 more source
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 $Φ(A^p)^
Audenaert, Koenraad M. R., Hiai, Fumio
openaire +2 more sources
Optimal sublinear inequalities involving geometric and power means [PDF]
Mathematica Bohemica, 2009 Summary: There are many relations involving the geometric means \(G_{n}(x)\) and power means \([A_{n}(x^{\gamma })]^{1/\gamma }\) for positive \(n\)-vectors \(x\). Some of them assume the form of inequalities involving parameters. There then is the question of sharpness, which is quite difficult in general.
Wen, Jiajin +2 more
openaire +2 more sources