Geodesic
Lower semi-Taylor mappings and sufficient conditions for an extremum
Sbornik. Mathematics, Tome 73 (1992) no. 1, pp. 257-271 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $(\tau,{\|\ \ \|})$-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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M. F. Sukhinin. Lower semi-Taylor mappings and sufficient conditions for an extremum. Sbornik. Mathematics, Tome 73 (1992) no. 1, pp. 257-271. http://geodesic.mathdoc.fr/item/SM_1992_73_1_a13/

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