JournalszaaVol. 15, No. 1pp. 201–222

On Multipower Equations: Some Iterative Solutions and Applications

  • David K. Ruch

    Sam Houston State University, Huntsville, USA
  • Patrick J. Van Fleet

    Sam Houston State University, Huntsville, USA
On Multipower Equations: Some Iterative Solutions and Applications cover
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Abstract

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.

Cite this article

David K. Ruch, Patrick J. Van Fleet, On Multipower Equations: Some Iterative Solutions and Applications. Z. Anal. Anwend. 15 (1996), no. 1, pp. 201–222

DOI 10.4171/ZAA/695