The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (1170 KB) | Metadata | Table of Contents | ZAA summary
Volume 15, Issue 1, 1996, pp. 201–222
DOI: 10.4171/ZAA/695

Published online: 1996-03-31

On Multipower Equations: Some Iterative Solutions and Applications

David K. Ruch[1] and Patrick J. Van Fleet[2]

(1) Sam Houston State University, Huntsville, USA
(2) Sam Houston State University, Huntsville, USA

generalization of McFarland’s iterative scheme [12] for solving quadratic equa-tions 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.

Keywords: Multipower equations, $k$-linear equations, uniformly contractive systems, Hammerstein equations, Chandrashekar equations, wavelets

Ruch David, Van Fleet Patrick: On Multipower Equations: Some Iterative Solutions and Applications. Z. Anal. Anwend. 15 (1996), 201-222. doi: 10.4171/ZAA/695