On Bellman's allocation processes
type: Item
instance of: scholarly article
title: On Bellman's allocation processes
zbMATH Open document ID: 0601.49022
DOI: 10.1016/0022-247X(85)90201-X
author: Seiichi Iwamoto
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The author considers the class of k-parametrized functional equations \[ f(x)=\max_{kx\leq y_ 1+y_ 2\leq x;\;y_ 1,y_ 2\geq 0}[g(y_ 1)+h(y_ 2)+f(x-(1-a)y_ 1-(1-b)y_ 2)],\quad x\geq 0,\;f(0)=0,\;0\leq k\leq 1, \] and their inversions \[ u(z)=\min_{kx\leq y_ 1+y_ 2\leq x;\;y_ 1,y_ 2\geq 0,\;x=f^{-1}(z)}[(1- a)y_ 1+(1-b)y_ 2+u(z-g(y_ 1)-h(y_ 2))],\quad z\geq 0,\;u(0)=0. \] Existence and uniqueness of the solution \(f\) resp. \(f^{-1}\) are discussed, and two successive approximation methods are suggested for computing the unique solution \(f^{-1}\).
reviewed by: Tadeusz J. Sawik
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 49L99
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 39B99
zbMATH DE Number: 3969492
zbMATH Keywords: inverse functional equations
zbMATH Keywords: inversion of dynamic programs
zbMATH Keywords: allocation processes
zbMATH Keywords: k-parametrized functional equations
MaRDI profile type: Publication
cites work: Q3241581
cites work: Inversion of dynamic programs and its applications to allocation processes
cites work: Q3317653
full work available at URL: 0022-247x(85)90201-x
OpenAlex ID: W1991616543
description: scientific article; zbMATH DE number 3969492