Abstract:
Sufficient conditions for an extremum of second-order type are considered on the basis of the concepts (introduced in the paper) of $(\tau,{\|\ \ \|})$-Taylor mappings and lower
$(\tau,{\|\ \ \|})$-semi-Taylor mappings, where ${\|\ \ \|}$ is a norm in a linear space $X$, and $\tau$ is a topology in a subset $U\subset X$. 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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