Integral representation of the global maximum point (Q1842424)

The author analyzes the sequence of vectors \[ x_ p= \int_{\pi_ n} xf^ p dx\;\Biggl( \int_{\pi_ n} f^ p dx\Biggr)^{- 1}, \] where \(f\) is a nonnegative bounded integrable function defined on the \(n\)- dimensional cube \(\pi_ n= \{x= (x^ 1,\dots, x^ n): -1\leq x^ i\leq 1\}\). The theorems of the paper state the approximation of the global maximum points of \(f\) on \(\pi_ n\) by the considered sequence.