On estimates of uniform approximations of some classes of functions by the Fourier – Chebyshev rational integral operator

The problem of finding new estimates of uniform approximations by the Fourier – Chebyshev rational integral operator on classes of Markov functions, functions with a power singularity, conjugate functions with a density having a power singularity, and singular integrals with a Cauchy kernel, Chebyshev weight of the second kind and density having a power singularity. In some cases, the estimates found have a greater descending order, in comparison with the previously known corresponding results.