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Uniqueness and the convergence of successive approximations. II

1965
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Proceedings of the American Mathematical Society
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It has long been known that the uniqueness of the solution of an ordinary differential problem of the type of (1) below and the convergence of sequences of successive approximations (Picard sequences) to solutions are logically independent. Thus Brauer and Sternberg [2] list examples (due to Müller and Dieudonné) in which there is uniqueness but not convergence or convergence but not uniqueness. Nevertheless, uniqueness and convergence are closely related, and we have recently shown [lO], for a

doi:10.1090/s0002-9939-1965-0201711-2
fatcat:tf3qsfjxmvaxzhrpkvkqo4ilva