On the asymptotic value of approximation Mellin singular integral in the summable function

Many questions about the order of approximation and their order of convergence of various classes of functions by linear operators, in particular singular integrals. Approximations of functions by singular integrals have numerous applications in various fields of mathematics. Approximations of functions by singular integrals are studied intensively along with other issues in theory of functions. In their papers PL Butzer and RG Mamedov study convergence order of singular integrals in generating functions at separate characteristic points and metric in the space on bounded and unbounded domains. Important theorems on asymptotic value of approximation of functions by singular integrals are obtained in these papers. In this paper, we study the approximation properties of the Mellin singular integral in terms of the mean oscillation of a locally summable function.