The criterion of the best approximant for the multivariable functions in the space $$$L_{p_1,...,p_{i-1},1,p_{i+1},...,p_n}$$$

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

The questions of the characterization of the best approximant in spaces with mixed integral metric with weight were considered in this article. The general form of a bounded linear functional and the criterion of best approximant in these spaces are obtained.

The questions of the characterization of the best nonsymmetric approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterion of best nonsymmetric approximant in these spaces is obtained.

The questions of the characterization of the best approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterions of the best approximant in spaces $L_{1,p_2,...,p_n}$ and $L_{p_1,...,p_{n-1},1}$ is obtained.

The general form of a linear functional and a criteria for a best approximation polynomial in a space with mixed integral metric

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