Turkish Journal Of Mathematics, cilt.44, sa.3, ss.1027-1041, 2020 (SCI İndekslerine Giren Dergi)
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.