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Zeitschrift für Analysis und ihre Anwendungen


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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