Korovkin-type theorems and their statistical versions in grand Lebesgue spaces

Abstract

The analogs of Korovkin theorems in grand-Lebesgue spaces are proved. The subspace G p −π; π of grand Lebesgue space is defined using shift operator. It is shown that the space of infinitely differentiable finite functions is dense in G p −π; π . The analogs of Korovkin theorems are proved in G p −π; π . These results are established in G p −π; π in the sense of statistical convergence. The obtained results are applied to a sequence of operators generated by the Kantorovich polynomials, to Fejer and Abel-Poisson convolution operators.