Results 41 to 50 of about 902,467 (342)

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

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   +3 more sources

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

Tight probablisitic MSE constrained multiuser MISO transceiver design under channel uncertainty [PDF]

, 2015
A novel optimization method is proposed to solve the probabilistic mean square error (MSE) constrained multiuser multiple-input single-output (MU-MISO) transceiver design problem.
He, X, Wu, YC
core   +1 more source

Improvement in Some Inequalities via Jensen-Mercer Inequality and Fractional Extended Riemann-Liouville Integrals

Axioms, 2023
The primary intent of this study is to establish some important inequalities of the Hermite–Hadamard, trapezoid, and midpoint types under fractional extended Riemann–Liouville integrals (FERLIs).
Abd-Allah Hyder, Areej A. Almoneef, H. Budak   +2 more
semanticscholar   +1 more source

Norm inequalities for weighted power means of operators

Linear Algebra and its Applications, 2002
Let \(A_{i}\), \(X_{i}\) and \(Y_{i}\) be bounded linear operators on a Hilbert space for \(i=1,2,\dots ,n\). In the present paper, the authors prove the following norm inequalities: (i) If \(\sum_{i=1}^{n}X^{*}_{i}X_{i}\leq I\), \(\sum_{i=1}^{n}Y^{*}_{i}Y_{ i}\leq I\) and \(r\geq 1\), then \[ \Bigg|\Bigg|\Bigg|\Bigg |\sum_{i =1}^{n} X_{i}^{*}A_{i}Y_{i}
Fuad Kittaneh, Omar Hirzallah
openaire   +2 more sources

New generalized integral inequalities with applications

AIMS Mathematics, 2019
The authors have proved an identity for a generalized integral operator via differentiable function. By applying the established identity, the generalized trapezium type integral inequalities have been discovered.
Artion Kashuri, Rozana Liko, Silvestru Sever Dragomir   +2 more
doaj   +1 more source

Hermite–Hadamard-type inequalities for geometrically r-convex functions in terms of Stolarsky’s mean with applications to means

Advances in Difference Equations, 2021
In this paper, we obtain new Hermite–Hadamard-type inequalities for r-convex and geometrically convex functions and, additionally, some new Hermite–Hadamard-type inequalities by using the Hölder–İşcan integral inequality and an improved power-mean ...
Muhammad Amer Latif
doaj   +1 more source

Structure of a generalized class of weights satisfy weighted reverse Hölder’s inequality

Journal of Inequalities and Applications, 2023
In this paper, we will prove some fundamental properties of the power mean operator M p g ( t ) = ( 1 ϒ ( t ) ∫ 0 t λ ( s ) g p ( s ) d s ) 1 / p , for  t ∈ I ⊆ R + , $$ \mathcal{M}_{p}g(t)= \biggl( \frac{1}{\Upsilon(t)} \int _{0}^{t} \lambda (s)g^{p ...
S. Saker, M. Zakarya, Ghada AlNemer, H. M. Rezk   +3 more
semanticscholar   +1 more source