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We obtain the criterion of the best non-symmetric approximant for two-variable functions in spaces with mixed integral metric.



We obtain the criterion of the best approximant for multivariable functions in Lp1,…pnL_{p_1,\ldots p_n} space.

We obtain the conditions of unicity of the best L1L_1-approximant for vector-valued functions, continuous on metric compact, by subspace of constant mappings.

The criterion of the best non-symmetric approximant for functions of many variables in the spaces with mixed integral metric is obtained.

The conditions of the unicity of the best nonsymmetric L1L_1-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

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