Lo-Keng Hua inequality and dynamic programming
type: Item
instance of: scholarly article
title: Lo-Keng Hua inequality and dynamic programming
zbMATH Open document ID: 0756.26014
DOI: 10.1016/0022-247X(92)90301-S
author: S. Singh
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: This paper states the Lo-Keng Hua inequality as \[ (\delta-x_ 1-\cdots- x_ n)^ 2+\alpha(x^ 2_ 1+\cdots+x^ 2_ n)\geq k_ n\delta^ 2 \tag{1} \] with equality if and only if \(x_ 1=\cdots=x_ n=h_ n\delta\), where \(k^ 2=\alpha(n+\alpha)^{-1}\), \(h_ n=(n+\alpha)^{- 1}\), \(\delta,\alpha>0\). Moreover, (1) is generalized to the inequality \[ (\delta-x_ 1-\cdots-x_ n)^ p+\alpha^{p-1}(x^ p_ 1+\cdots+x^ p_ n)\geq k_ n^{p-1}\delta^ p,\;p\geq 0, \] and its continuous counterpart. Two proofs for either inequality are presented.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 62818
zbMATH Keywords: dynamic programming
zbMATH Keywords: Hölder-Lorentz inequality
zbMATH Keywords: Lo-Keng Hua inequality
MaRDI profile type: Publication
cites work: Q5336417
cites work: Q3241581
cites work: Functional equations in dynamic programming
cites work: Q3234755
cites work: Q5587215
cites work: Continuous dynamic programming approach to inequalities
cites work: Continuous dynamic programming approach to inequalities. II
cites work: Some theorems on reverse inequalities
cites work: Functional equation approach to inequalities. VI
cites work: Characteristics of nonlinear positive functionals and their applications
cites work: The principle and models of dynamic programming
cites work: The principle and models of dynamic programming. IV
full work available at URL: 0022-247x(92)90301-s
OpenAlex ID: W2005591986
Recommended article: Dynamic programming and inequalities
Recommended article: A generalization of the Hölder inequality through dynamic programming approach
Recommended article: Q4856101
Recommended article: Dynamic programming and the Lagrange multipliers
Recommended article: On Bounds for Dynamic Programs
Recommended article: A Uniform Tauberian Theorem in Dynamic Programming
Recommended article: A remark on the Lo-Keng Hua inequality
Recommended article: Bounds for the approximation of dynamic programs
Recommended article: Q4838437
Recommended article: Q2996937
description: scientific article; zbMATH DE number 62818