On a class of nonChebyshev function systems allowing to use Markov theorem in the finite moment problem

The class indicated in the header is formed by degrees of a unimodal continuous function, whose several successive powers of the left branch on the corresponding interval of its definition is Chebyshev system. It turns out that both maximum and minimum of a specific integral with some unknown function can be obtained using the Markov theorem in which the weights and nodes are found only with the help of the left branch. The need for such estimates naturally arises from the simplest problem of nonlinear dynamics such as iterations of a unimodal function with unknown distribution of the initial value and its known polynomial moments of the next iteration step.