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Sufficient conditions for an extremum of second-order type are considered on the basis of the concepts (introduced in the paper) of -Taylor mappings and lower -semi-Taylor mappings, where is a norm in a linear space , and is a topology in a subset . Examples are given illustrating the novelty of the results obtained. Among the references devoted to sufficient conditions for an extremum, [1] (§3.4) and [2] (§6) should be mentioned.
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M. F. Sukhinin (1992) studied this question.
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