Geodesic
Extremums of vector-valued functions of several real variables
Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 119-134.

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In this paper we try to give a generalization of the usual notion of extremum of real functions to the vector-valued functions of several real variables. Our aim is that in this generalization remain valid the usual properties and relations for extremum of real functions. A considered generalization is also characterized by an equivalent generalization. Our definitions and related results are illustrated by numerous examples. 
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     author = {Jela \v{S}u\v{s}i\'c},
     title = {Extremums of vector-valued functions of several real variables},
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Jela Šušić. Extremums of vector-valued functions of several real variables. Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 119-134. http://geodesic.mathdoc.fr/item/CHEB_2013_14_1_a11/

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[2] Arhipov G. I., Sadovničij V. A., Čubarikov V. N., Lekcii po matematicheskomu analizu, v. II, MSU, M., 1997 (in Russian)