A generalization of the Hölder inequality through dynamic programming approach
type: Item
instance of: scholarly article
title: A generalization of the Hölder inequality through dynamic programming approach
zbMATH Open document ID: 0665.26005
DOI: 10.1016/0022-247X(88)90138-2
author: Seiichi Iwamoto
author: Chung-Lie Wang
author: R. James Tomkins
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: This paper generalizes the Hölder inequality to one with ordered constraint and with lower bound through dynamic programming (DP) approach. \textit{G. S. Mudholker, M. Freimer} and \textit{P. Subbaiah} [J. Math. Anal. Appl. 102, 435-441 (1984; Zbl 0563.26013)] extended the Hölder inequality to one with the ordered constraint by Lagrange's multiplier method, and \textit{M. Freimer} and \textit{G. S. Mudholker} [Proc. Sympos. Inequalities in statistics and probability, IMS Lecture-Notes- Monograph, Ser. 5, 59-67 (1984)] generalized it by use of Kuhn-Tucker condition in mathematical programming. Later, the authors generalized the Hölder inequality by applying a majorization theorem. In this paper, the authors extend further the generalized Hölder inequality to one with the ordered constraint and with a lower parametric bound by solving three pairs of main (maximum) and inverse (minimum) DP problems without appealing to majorization theorem of any kind.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 4087945
zbMATH Keywords: dynamic programming approach
zbMATH Keywords: inverse problem
zbMATH Keywords: Hölder inequality
zbMATH Keywords: ordered constraint
zbMATH Keywords: lower parametric bound
MaRDI profile type: Publication
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full work available at URL: 0022-247x(88)90138-2
OpenAlex ID: W2004555881
description: scientific article; zbMATH DE number 4087945