On multipower equations: Some iterative solutions and applications
type: Item
instance of: scholarly article
title: On multipower equations: Some iterative solutions and applications
zbMATH Open document ID: 0841.47038
DOI: 10.4171/ZAA/695
author: David Ruch
author: Patrick J. Van Fleet
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-05-09T00:00:00Z
review text: Summary: A generalization of \textit{J. E. McFarland's} iterative scheme [Proc. Am. Math. Soc. 9, 824-830 (1958; Zbl 0092.12202)] for solving quadratic equations in Banach spaces is reported. The notion of a uniformly contractive system is introduced and subsequently employed to investigate the convergence of a new iterative method for approximating solutions to this wider class of multipower equations. Existence and uniqueness of solutions are addressed within the framework of a uniformly contractive system. To illustrate the use of the new iterative scheme, we employ it when approximating solutions to a Hammerstein equation and a Chandrashekar equation. Due to the nature of the examples, we have found that wavelet/scaling function bases are a natural choice for the implementation of our iterative method.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 46N20
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 856813
zbMATH Keywords: \(k\)-linear equations
zbMATH Keywords: wavelets
zbMATH Keywords: McFarland's iterative scheme
zbMATH Keywords: uniformly contractive system
zbMATH Keywords: iterative method
zbMATH Keywords: multipower equations
zbMATH Keywords: Hammerstein equation
zbMATH Keywords: Chandrashekar equation
zbMATH Keywords: wavelet/scaling function bases
MaRDI profile type: Publication
cites work: Quadratic equations and applications to Chandrasekhar's and related equations
cites work: Q4318613
cites work: Q4003151
cites work: Q4328441
cites work: Wavelets on the interval and fast wavelet transforms
cites work: Ten Lectures on Wavelets
cites work: Orthonormal bases of compactly supported wavelets
cites work: Q3994824
cites work: Q5531285
cites work: Positive Solutions of Negative Exponent Generalized Emden–Fowler Boundary Value Problems
cites work: An Iterative Solution of the Quadratic Equation in Banach Space
cites work: Ondelettes sur l'intervalle. (Wavelets on the interval)
cites work: Q5186213
cites work: Q5655975
cites work: Q5563748
cites work: Characterizations of compact bilinear maps
cites work: On uniformly contractive systems and quadratic equations in Banach space
cites work: Completely continuous and related multilinear operators
description: scientific article; zbMATH DE number 856813