Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1996-03-31
On Multipower Equations: Some Iterative Solutions and ApplicationsDavid K. Ruch and Patrick J. Van Fleet (1) Sam Houston State University, Huntsville, USA
(2) Sam Houston State University, Huntsville, USA
generalization of McFarland’s iterative scheme  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