On multipower equations: Some iterative solutions and applications
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.
scientific article; zbMATH DE number 856813
scientific article