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On uniformly contractive systems and quadratic equations in Banach space

Published online by Cambridge University Press:  17 April 2009

David K. Ruch
David K. Ruch
Affiliation:
Department of MathematicsSam Houston State UniversityHuntsvilleTX 77341United States of America
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Abstract

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The solution of quadratic equations using the contraction mapping principle is considered. A uniqueness result extending that given by Argyros is proved. Uniformly contractive systems theory is used to find approximate solutions and convergence criteria are given. In particular, only pointwise convergence of approximating operators is required to guarantee convergence of the approximate solutions. A theorem and algorithm for a continuation method are presented, and illustrated on Chandrasekhar's equation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 3 , December 1995 , pp. 441 - 455
Copyright
Copyright © Australian Mathematical Society 1995

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