ON THE APPLICATION OF ANALOGUES OF THEKOROVKIN THEOREM TO THE CONVERGENCE OFCERTAIN CLASSES OF SEQUENCES OF CONVOLUTIONOPERATORS

This paper establishes conditions on the Young function and the summability exponent p() that ensure the validity of analogues of Korovkin's theorem for sequences of positive convolution operators in Orlicz spaces L and Lebesgue spaces L p () with a variable summability exponent.The results obtained in the space L are applied to the convergence of a sequence of Fejer and Poisson operators.Also, using the obtained result, the convergence of the family of Fejer and Steklov operators to the unit operator in the space L p () is established.