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A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations. (English) Zbl 0599.34008
We point out a flaw in the proof of the results of W. J. Knight, Bull. Am. Math. Soc. 80, 148-149 (1974; Zbl 0281.34057) and we mend it using a fixed point theorem for sequentially weakly continuous mappings which has its own interest.

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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