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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Product integral approximations of solutions to linear operator equations

Author: Robert H. Martin
Journal: Proc. Amer. Math. Soc. 41 (1973), 506-512
MSC: Primary 47A50; Secondary 45A05
MathSciNet review: 0380463
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Abstract: In the paper we develop a class of iterative methods for approximating solutions of linear operator equations in a Banach space. The main techniques involve a product integral representation of solutions to linear Stieltjes integral equations, a variation of parameters formula, and the asymptotic convergence of solutions to the homogeneous integral equation.

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Keywords: Linear operator equations, product integral, Stieltjes integral equation, asymptotic convergence
Article copyright: © Copyright 1973 American Mathematical Society